Morphological synergism in root hair length, density, initiation and geometry for phosphorus acquisition in Arabidopsis thaliana: A modeling approach

Low phosphorus availability regulates root hair growth in Arabidopsis by (1) increasing root hair length, (2) increasing root hair density, (3) decreasing the distance between the root tip and the point at which root hairs begin to emerge, and (4) increasing the number of epidermal cell files that bear hairs (trichoblasts). The coordinated regulation of these traits by phosphorus availability prompted us to speculate that they are synergistic, that is, that they have greater adaptive value in combination than they do in isolation. In this study, we explored this concept using a geometric model to evaluate the effect of varying root hair length (short, medium, and long), density (0, 24, 48, 72, 96, and 120 root hairs per mm of root length), tip to first root hair distance (0.5, 1, 2, and 4 mm), and number of trichoblast files (8 vs. 12) on phosphorus acquisition efficiency (PAE) in Arabidopsis. SimRoot, a dynamic threedimensional geometric model of root growth and architecture, was used to simulate the growth of Arabidopsis roots with contrasting root hair parameters at three values of phosphorus diffusion coefficient (D_e=1 × 10^-7, 1 × 10^-8, and 1 × 10^-9 cm² s^-1) over time (20, 40, and 60 h). Depzone, a program that dynamically models nutrient diffusion to roots, was employed to estimate PAE and competition among root hairs. As D_e decreased from 1 × 10^-7 to 1 × 10^-9 cm² s^-1, roots with longer root hairs and higher root hair densities had greater PAE than those with shorter and less dense root hairs. At D_e=1 × 10^-9 cm² s^-1, the PAE of root hairs at any given density was in the order of long hairs > medium length hairs > short hairs, and the maximum PAE occurred at density = 96 hairs mm^-1 for both long and medium length hairs. This was due to greater competition among root hairs when they were short and dense. Competition over time decreased differences in PAE due to density, but the effect of length was maintained, as there was less competition among long hairs than short hairs. At high D_e(1 × 10^-7 cm² s^-1), competition among root hairs was greatest among long hairs and lowest among short hairs, and competition increased with increasing root hair densities. This led to a decrease in PAE as root hair length and density increased. PAE was also affected by the tip to first root hair distance. At low D_e values, decreasing tip to first root hair distance increased PAE of long hairs more than that of short hairs, whereas at high De values, decreasing tip to first root hair distance increased PAE of root hairs at low density but decreased PAE of long hairs at very high density. Our models confirmed the benefits of increasing root hair density by increasing the number of trichoblast files rather than decreasing the trichoblast length. The combined effects of all four root hair traits on phosphorus acquisition was 371% greater than their additive effects, demonstrating substantial morphological synergy. In conclusion, our data support the hypothesis that the responses of root hairs to low phosphorus availability are synergistic, which may account for their coordinated regulation.