Growth-induced hormone dilution can explain the dynamics of plant root cell elongation

Abstract

In the elongation zone of the Arabidopsis thaliana plant root, cells undergo rapid elongation, increasing their length by ∼10-fold over 5 h while maintaining a constant radius. Although progress is being made in understanding how this growth is regulated, little consideration has been given as to how cell elongation affects the distribution of the key regulating hormones. Using a multiscale mathematical model and measurements of growth dynamics, we investigate the distribution of the hormone gibberellin in the root elongation zone. The model quantifies how rapid cell expansion causes gibberellin to dilute, creating a significant gradient in gibberellin levels. By incorporating the gibberellin signaling network, we simulate how gibberellin dilution affects the downstream components, including the growth-repressing DELLA proteins. We predict a gradient in DELLA that provides an explanation of the reduction in growth exhibited as cells move toward the end of the elongation zone. These results are validated at the molecular level by comparing predicted mRNA levels with transcriptomic data. To explore the dynamics further, we simulate perturbed systems in which gibberellin levels are reduced, considering both genetically modified and chemically treated roots. By modeling these cases, we predict how these perturbations affect gibberellin and DELLA levels and thereby provide insight into their altered growth dynamics.

Fig. 1.

Model summary. (A) Schematic representation of the Arabidopsis plant root showing the meristem, elongation zone, and mature zone (MZ). The red arrowhead indicates the position of the xylem formation/first root hair bulge, taken to be the end of the elongation zone. (B) Each cell consists of a cytoplasm (white), containing the nucleus (red) and the vacuole (blue), which is enclosed within the tonoplast. The cytoplasm is surrounded by a plasma membrane, which is embedded within the fibrous cell wall (black). (C) The gibberellin signaling network. In the network diagram, circular symbols are used for the hormone gibberellin (GA), rectangular symbols for proteins, and hexagonal symbols for mRNAs.

Fig. 2.

The elongation zone (EZ) dynamics in Arabidopsis plant roots. (A) Experimental data of cortical cell lengths through the elongation zone, l(x), for wild-type roots (Columbia ecotype). Data from each file of cortical cells are plotted with a different symbol. The line shows the average of the data. (B) Evolution of each cell's length as it passes through the elongation zone, L_i(t), obtained via Eq. 1. (C) Predicted fold changes in gibberellin (GA) and DELLA concentrations and GID1 and DELLA mRNA levels. (D) Measured mRNA expression of the GID1 family members, GID1a and GID1b, and of the two DELLAs important in the root, RGA and GAI, for the elongation zone (EZ; from the top of the lateral root cap to the first visible root hair bulge, ∼850 μm from the top of the lateral root cap) and the decelerating elongation zone (DZ; from the first root hair bulge to the first fully elongated root hair). Within each zone, gene expression is normalized relative to ACT2 (a standard housekeeping gene). We present fold changes of these values relative to the elongation zone values.

Fig. 3.

The elongation zone dynamics in paclobutrazol-treated Arabidopsis plant roots. (A) Six-day-old Arabidopsis seedlings (Columbia ecotype) treated with 0, 1, and 5 μM paclobutrazol (PAC). (B) Averaged cell length measurements through the elongation zone, l(x), with error bars showing the SE. (C) Time interval between successive cells entering the elongation zone, with error bars showing the SE. (D) Evolution of each cell's length, L_i(t). (E) Evolution of each cell's RER, 1/L_idL_i/dt. (F) Predicted gibberellin concentrations. (G) Predicted DELLA concentrations. (H) Predicted fold change in DELLA. (I) Relationship between fold change in DELLA and RER in control, paclobutrazol-treated, and mutant plant roots.

Fig. 4.

The elongation zone dynamics in gibberellin-deficient Arabidopsis plant roots. (A) Six-day-old Arabidopsis seedlings, Landsberg ecotype (Control); gibberellin-biosynthesis mutants, ga1-3; and mutants in both gibberellin biosynthesis and loss of DELLA function, ga1-3/gai-t6/rga24. (Bar: 1 cm.) (B) Averaged cell length measurements through the elongation zone, l(x), with error bars showing the SE. (C) Time interval between successive cells entering the elongation zone, with error bars showing the SE. (D) Evolution of each cell's length, L_i(t). (E) Evolution of each cell's RER, 1/L_idL_i/dt. (F) Predicted gibberellin concentrations. (G) Predicted DELLA concentrations. (H) Predicted fold change in DELLA.