Continuum mechanics of plant growth and morphogenesis

Plant growth is a mechanical process that depends on the stresses generated by turgor pressure and the ability of cells to alter the mechanical properties of their wall to allow growth. In this thesis, I present a continuum mechanics approach to growth and morphogenesis in single cells and multicellular structures. I first introduce equations to describe the relation between the mechanical properties of the cell wall and the growth of cells. Cell wall mechanics is modeled as the deformation of an anisotropic viscoplastic material under multiaxial stress. The theory generalizes Bingham's equation so as to capture the effect of coupling between different directions of extension on the apparent mechanical properties of the cell wall. This model is applied to wall extension in root hairs of Medicago truncatula. The measured extension rates and computed turgor stresses are compatible with the idea that the cell wall is mechanically isotropic in its plane. To extend this approach to multicellular structures, I developed a protocol for the analysis of growth in 3-D. The protocol uses a nondestructive replica method to follow the pattern of cell expansion and divisions over several days. Algorithms to reconstruct the surface of the structure under investigation and to compute its curvature and rate of extension were implemented. This approach was applied to the shoot apical meristem of Anagallis arvensis to give the first detailed quantitative analysis of meristem growth in 3-D. Finally, I address a related problem, that of the initiation of lateral organs at the shoot apical meristem. I tested one critical feature of a buckling mechanism of organ initiation, i.e. the presence of compressive stresses in the meristem. Direct evidence for compression in the sunflower capitulum was obtained from the gaping pattern of shallow cuts and the propagation of fractures. This conclusion was confirmed by the stress distribution computed from the geometry of the capitulum at three stages of development. One interpretation of these results is that the generative region corresponds to a zone of compression which could control the initiation of new primordia via buckling of the tunica layer.