A Model Analysis of Mechanisms for Radial Microtubular Patterns at Root Hair Initiation Sites

Abstract

Plant cells have two main modes of growth generating anisotropic structures. Diffuse growth where whole cell walls extend in specific directions, guided by anisotropically positioned cellulose fibers, and tip growth, with inhomogeneous addition of new cell wall material at the tip of the structure. Cells are known to regulate these processes via molecular signals and the cytoskeleton. Mechanical stress has been proposed to provide an input to the positioning of the cellulose fibers via cortical microtubules in diffuse growth. In particular, a stress feedback model predicts a circumferential pattern of fibers surrounding apical tissues and growing primordia, guided by the anisotropic curvature in such tissues. In contrast, during the initiation of tip growing root hairs, a star-like radial pattern has recently been observed. Here, we use detailed finite element models to analyze how a change in mechanical properties at the root hair initiation site can lead to star-like stress patterns in order to understand whether a stress-based feedback model can also explain the microtubule patterns seen during root hair initiation. We show that two independent mechanisms, individually or combined, can be sufficient to generate radial patterns. In the first, new material is added locally at the position of the root hair. In the second, increased tension in the initiation area provides a mechanism. Finally, we describe how a molecular model of Rho-of-plant (ROP) GTPases activation driven by auxin can position a patch of activated ROP protein basally along a 2D root epidermal cell plasma membrane, paving the way for models where mechanical and molecular mechanisms cooperate in the initial placement and outgrowth of root hairs.

Mechanical Behavior of Cells within a Cell-Based Model of Wheat Leaf Growth

“…Estimates of the cell wall Young's modulus, E , from the literature vary from ≈ 1 to 10, 000 bar (Krupinski et al, 2016); in our simulations, we used E = 1000 bar. To estimate the coefficient for turgor pressure from Equation (8), β, we used equation $\beta =\frac{S_w}{S_c}E=\frac{4r·d_w}{r^2}E$, assuming r = 4μm and d w = 0.1 μm.…”

Mathematical principles and models of plant growth mechanics: from cell wall dynamics to tissue morphogenesis

“…microtubules (Krupinski et al 2016). More evidence is found in sepals where microtubules have been shown to align with maximal tension in sepals (Hervieux et al 2016).…”

The Plasma Membrane—An Integrating Compartment for Mechano-Signaling

“…Indeed, plant development is the result of three essential processes: cell expansive growth, cell division and cellular differentiation, and these three phenomena were described and explained according to the laws of physics [87,88]). Molecular players involved in polar growth of root hairs and pollen tubes are well-described but recent studies revisited these models using mechanics as a new angle to understand how root hairs or pollen tubes are able to physically invade the soil or the stigmatic papillae, respectively [89][90][91]. Similarly, knowledge on biotic and abiotic stresses can be revisited when considering cell mechanics.…”