Simulating Turgor-Induced Stress Patterns in Multilayered Plant Tissues

Abstract

The intertwining between mechanics and developmental biology is extensively studied at the shoot apical meristem of land plants. Indeed, plants morphogenesis heavily relies on mechanics; tissue deformations are fueled by turgor-induced forces, and cell mechanosensitivity plays a major regulatory role in this dynamics. Since measurements of forces in growing meristems are still out of reach, our current knowledge relies mainly on theoretical and numerical models. So far, these modeling efforts have 1 been mostly focusing on the epidermis, where aerial organs are initiated. In many models, the epidermis is assimilated to its outermost cell walls and described as a thin continuous shell under pressure, thereby neglecting the inner walls. There is, however, growing experimental evidence suggesting a significant mechanical role of these inner walls. The aim of this work is to investigate the influence of inner walls on the mechanical homeostasis of meristematic tissues. To this end, we simulated numerically the effect of turgor-induced loading, both in realistic flower buds and in more abstract structures. These simulations were performed using finite element meshes 2 with subcellular resolution. Our analysis sheds light on the mechanics of growing plants by revealing the strong influence of inner walls on the epidermis mechanical stress pattern especially in negatively curved regions. Our simulations also display some strong and unsuspected features, such as a correlation between stress intensity and cell size, as well as differential response to loading between epidermal and inner cells. Finally, we monitored the time evolution of the mechanical stresses felt by each cell and its descendants during the early steps of flower morphogenesis.

Integration of Core Mechanisms Underlying Plant Aerial Architecture

“…Considering known estimates of the thickness of the Arabidopsis SAM outer cell wall, the authors estimated a stiffness ratio of outer to inner walls to be in the range of 3–10:1. Given these ratios, simulations demonstrate that the periclinal stress patterns (i.e., parallel to the tissue surface) in the outer walls of multilayered SAM models resemble those produced by shell models, thus validating earlier approaches ( Ali et al, 2019 ). A second important conclusion from this work is that maximal stress patterns in the anticlinal walls (i.e., perpendicular to the tissue surface) of both the epidermis and underlying cell layers are predominantly oriented anticlinally ( Ali et al, 2019 ), again matching observed microtubule and cellulose orientations ( Sakaguchi et al, 1988 ; Figure 1B ).…”

“…Given these ratios, simulations demonstrate that the periclinal stress patterns (i.e., parallel to the tissue surface) in the outer walls of multilayered SAM models resemble those produced by shell models, thus validating earlier approaches ( Ali et al, 2019 ). A second important conclusion from this work is that maximal stress patterns in the anticlinal walls (i.e., perpendicular to the tissue surface) of both the epidermis and underlying cell layers are predominantly oriented anticlinally ( Ali et al, 2019 ), again matching observed microtubule and cellulose orientations ( Sakaguchi et al, 1988 ; Figure 1B ). This a priori indicates that loosening the walls of subepidermal cells or randomizing cellulose orientations may result in anticlinal cellular growth, which would account for the initial outward bulge associated with lateral organ formation (see further discussion on auxin’s influence on microtubules see below).…”

“…Apart from finding that the stress/cell wall feedback loop operates in additional tissue contexts ( Sampathkumar et al, 2014 ; Hervieux et al, 2017 ; Belteton et al, 2021 ), an important recent advance has been in developing mechanical models to simulate more complex tissue structures. Rather than assuming pressurized shells, multilayered tissue models have been constructed and compared to simpler models ( Ali et al, 2019 ). Perhaps the most important conclusion from this work has been that the degree to which multilayered models generate similar surface stress patterns to those of shell models depends on the relative stiffness of inner cell layer walls compared to the outer epidermal cell layer walls.…”

Mechanical feedback-loop regulation of morphogenesis in plants

“…2011; Hervieux et al, 2017;Fox et al, 2018;Ali et al, 2019). Abstraction of cellular-scale FEM to a continuous sheet of material with defined cell scale information is also used to discretize tissuelevel details for simulation purposes (Bozorg et al, 2014;Hervieux et al, 2017;Kennaway and Coen, 2019).…”

In vitro experiments and kinetic models of pollen hydration show that MSL8 is not a simple tension-gated osmoregulator

“…However, at the cellular scale, plant mechanobiology is affected by physical connections to neighboring cells. Wall-to-wall adhesion adds external forces and responses that complicate mechanical characterization of any one cell 5,6 . Here, we employ pollen grains as a neighbor-less model system for biomechanical characterization of plant cells.…”