A balance of metabolism and diffusion articulates a gibberellin hormone gradient in the Arabidopsis root

Abstract

The plant hormone gibberellin (GA₄) regulates numerous developmental processes. Within the root, GA₄ controls growth, in part, by controlling the extent of cell elongation. The nlsGPS1 FRET biosensor revealed a GA₄ gradient within the Arabidopsis root growth zones, with GA₄ levels correlating with cell length. We developed a multiscale mathematical model to understand how biosynthesis, catabolism, and transport create the GA₄ distribution within the root growth zones. The model predicted that phloem delivery of the biosynthetic intermediate GA₁₂ contributes to higher levels of bioactive GA₄ in the elongation zone, with the GA₄ synthesis pattern being further modified by local GA₁₂ synthesis in the quiescent center region and the spatial distribution of biosynthesis enzymes (GA20ox and GA3ox). Model predictions suggested that while GA20ox and GA3ox transcript is present throughout the growth zones, these enzymes are inactive in the dividing cells, which explains steep GA₄ gradients observed in the GA3ox overexpression line and improves agreement between model predictions and data in wildtype. The model suggested that the GA₄ gradient also depends on a balance of diffusion through plasmodesmata and catabolism. Both model predictions and biosensor data demonstrated that plasmodesmatal diffusion enables a more gradual GA₄ gradient, with higher diffusion antagonizing the GA₄ gradient. Model predictions suggested that catabolism limits GA₄ levels, which we validated via biosensor imaging in the ga2oxhept mutant. In conclusion, our results suggest that local GA₄ synthesis combines with diffusion and catabolism to create a spatial GA₄ gradient that provides positional information and patterns cell elongation.

Keywords: Arabidopsis root development; gibberellin; hormone biosensor; multiscale modeling; plant hormones.

Fig. 1.

(A) Confocal image of the Arabidopsis root growth zones, together with a to-scale schematic of the modeled domain, showing the positions of the different zones. The model is one-dimensional, with $x=0$ positioned at the quiescent center (QC). (B) Schematic of the pathway downstream of GA₁₂ that mediates the biosynthesis and catabolism of GA₄, together with data showing the relative transcript levels of the enzymes, GA20ox, GA3ox, and GA2ox (showing separately the levels for GA2ox mediating GA₁₂ degradation and for GA2ox mediating GA₉ and GA₄ degradation) (5, 7). (C) Schematic focusing on a single cell showing the cell compartments, the transport components, and the localization of the NPF transporters. (D) Continuum governing equations for each metabolite, $j=12,15,24,9,$ and $4$. The equations for each metabolite are coupled through their production and degradation terms, $S_j(x,t)$, which represent the metabolic pathway depicted in Fig. 1B, and correspond to formulae given in SI Appendix, section 5.

Fig. 2.

Model predictions can reproduce GA₄ gradient observed using the nlsGPS1 sensor. (A and B) Predicted GA₁₂, GA₁₅, GA₂₄, GA₉, and GA₄ distributions due to (A) local GA₁₂ synthesis in the QCZ, and (B) GA₁₂ delivery in the phloem-unloading zone. (C) Predicted GA₄ distribution (due to both GA₁₂ delivery in the phloem-unloading zone), together with predictions in which either the GA₁₂ synthesis rate in the QCZ is doubled, or the GA₁₂ delivery rate in the phloem-unloading zone is doubled. (D) Comparison between the predicted and observed distribution of nlsGPS1 emission ratios. Predicted sensor distribution is calculated from the base case GA₄ distribution shown in panel (C). The experimental data are reproduced from figure 1F in ref. giving nlsGPS1 emission ratios from nuclei between 0 to 500 $\mathrm{\mu }$m from the root tip. Quantification of the difference between the predictions and data, Mean-Squared-Error, $\text{MSE}=0.0154$ (SI Appendix, section 7).

Fig. 3.

Enzyme inactivation in the division zone is essential to explain the sensor distributions in the GA20ox and GA3ox overexpression. (A–D) Experimental nlsGPS1 distributions reproduced from figure 1B and figure 2B,D,E in ref. . (E–L) Predicted nlsGPS1 emission ratio of GA₄ for (E and I) GA20ox overexpression, (F and J) GA3ox overexpression, (G and K) both GA20ox and GA3ox overexpression, and (H and L) ga20ox and ga3ox mutants. (E–H) Model predictions with enzyme activities based on transcript levels (shown in Fig. 1B). (I–L) Model predictions in which the GA20ox and GA3ox activity is set to zero in the DZ (with all other enzyme activities based on the transcript level). Model predictions with alternative assumptions are provided in SI Appendix, Fig. S8. Quantification of the difference between the predictions and data are provided in SI Appendix, Table S6.

Fig. 4.

Model predictions with inactive GA20ox and GA3ox in the DZ reproduce GA₄ gradient observed using the nlsGPS1 sensor (A and B) Predicted GA₁₂, GA₁₅, GA₂₄, GA₉, and GA₄ concentration distributions due to (A) GA₁₂ synthesis in the QCZ and (B) GA₁₂ delivery the phloem-unloading zone. (C) Predicted GA₄ distribution (due to both GA₁₂ delivery in the phloem-unloading zone), together with predictions in which either the GA₁₂ synthesis rate in the QCZ is doubled, or the GA₁₂ delivery rate in the phloem-unloading zone is doubled. (D) Comparison between predicted and observed distribution of nlsGPS1 emission ratios. Predicted sensor distribution is calculated from the base case GA₄ distribution shown in panel (C). The experimental data are reproduced from figure 1F in ref. giving nlsGPS1 emission ratios from nuclei between 0 to 500 $\mathrm{\mu }$m from the root tip. Quantification of the difference between the predictions and data, Mean-Squared-Error, $\text{MSE}=0.0124$ (SI Appendix, section 7).

Fig. 5.

The GA₄ gradient depends on plasmodesmatal diffusion and catabolism. (A) Predicted effect of the plasmodesmatal permeability, $P_{\mathrm{plas}}$, on the GA₄ distribution. (B and C) Representative images of nlsGPS2 emission ratios and YFP fluorescence (Inset) for pretreated (B) and $2$h $0.6$mM H₂O₂ treated (C) roots. Treatment used to show the effect of increasing plasmodesmata permeability. (Scale bar, 100 $\mathrm{\mu }$m applies to all images.) (D) Quantification of nlsGPS2 emission ratio data for pretreated and $2$h $0.6$mM H₂O₂ treated roots. Data quantified from images shown in panels (B and C), and SI Appendix, Fig. S12. (E) Predicted GA₄ distribution for the ga2ox heptuple mutant (with reduced degradation of GA₁₂, GA₉ and GA₄), (F and G) Representative images of nlsGPS2 emission ratios and YFP fluorescence (Inset) for Col0 (F) and ga2oxhept mutant (G) roots. (H) Quantification of nlsGPS2 emission ratio data for the ga2ox hept mutant. Data quantified from images shown in panels (F and G), and SI Appendix, Fig. S16. Panels (D and H) also show curves of best fit and 95% CIs for each dataset computed in R using local polynomial regression (Loess) via ggplot, with smoothing parameter span $=$ 0.75 (as in ref. 5).