Stress and Strain Provide Positional and Directional Cues in Development

The morphogenesis of organs necessarily involves mechanical interactions and changes in mechanical properties of a tissue. A long standing question is how such changes are directed on a cellular scale while being coordinated at a tissular scale. Growing evidence suggests that mechanical cues are participating in the control of growth and morphogenesis during development. We introduce a mechanical model that represents the deposition of cellulose fibers in primary plant walls. In the model both the degree of material anisotropy and the anisotropy direction are regulated by stress anisotropy. We show that the finite element shell model and the simpler triangular biquadratic springs approach provide equally adequate descriptions of cell mechanics in tissue pressure simulations of the epidermis. In a growing organ, where circumferentially organized fibers act as a main controller of longitudinal growth, we show that the fiber direction can be correlated with both the maximal stress direction and the direction orthogonal to the maximal strain direction. However, when dynamic updates of the fiber direction are introduced, the mechanical stress provides a robust directional cue for the circumferential organization of the fibers, whereas the orthogonal to maximal strain model leads to an unstable situation where the fibers reorient longitudinally. Our investigation of the more complex shape and growth patterns in the shoot apical meristem where new organs are initiated shows that a stress based feedback on fiber directions is capable of reproducing the main features of in vivo cellulose fiber directions, deformations and material properties in different regions of the shoot. In particular, we show that this purely mechanical model can create radially distinct regions such that cells expand slowly and isotropically in the central zone while cells at the periphery expand more quickly and in the radial direction, which is a well established growth pattern in the meristem.Author Summary: Development and morphogenesis of tissues are dependent on a coordination between cell differentiation, proliferation and growth. Plants, which lack cell migration, control directional growth of tissues by adjusting cellulose fiber directions so forming the organ shapes. It has recently been shown that mechanical cues can guide these fibers. We developed detailed mechanical models to investigate how fiber directions may be responding to mechanical cues and what consequences this may have for positional and directional growth patterns. We show that a model in which fibers align to maximal stress directions spontaneously generates a radial zonation in the shoot, recapitulating the slowly growing center and more rapidly growing peripheral region previously observed in the meristem. These radial patterns emerging from mechanics are in striking correspondence to the expression patterns of the genes important for stem cell maintenance, which attain similar radial domains. We also show that the stress model can robustly define anisotropically growing organs, which emphasizes the potential importance of stress in generating correct organ shapes in plants.