Ptashnyk Mariya, Seguin Brian
Division of Mathematics, University of Dundee, Dundee, DD1 4HN, UK.
Department of Mathematics and Statistics, Loyola University Chicago, Chicago, IL, 60660, USA.
Bull Math Biol. 2016 Nov;78(11):2135-2164. doi: 10.1007/s11538-016-0207-8. Epub 2016 Oct 19.
The microscopic structure and anisotropy of plant cell walls greatly influence the mechanical properties, morphogenesis, and growth of plant cells and tissues. The microscopic structure and properties of cell walls are determined by the orientation and mechanical properties of the cellulose microfibrils and the mechanical properties of the cell wall matrix. Viewing the shape of a plant cell as a square prism with the axis aligning with the primary direction of expansion and growth, the orientation of the microfibrils within the side walls, i.e. the parts of the cell walls on the sides of the cells, is known. However, not much is known about their orientation at the upper and lower ends of the cell. Here we investigate the impact of the orientation of cellulose microfibrils within the upper and lower parts of the plant cell walls by solving the equations of linear elasticity numerically. Three different scenarios for the orientation of the microfibrils are considered. We also distinguish between the microstructure in the side walls given by microfibrils perpendicular to the main direction of the expansion and the situation where the microfibrils are rotated through the wall thickness. The macroscopic elastic properties of the cell wall are obtained using homogenization theory from the microscopic description of the elastic properties of the cell wall microfibrils and wall matrix. It is found that the orientation of the microfibrils in the upper and lower parts of the cell walls affects the expansion of the cell in the lateral directions and is particularly important in the case of forces acting on plant cell walls and tissues.
植物细胞壁的微观结构和各向异性极大地影响着植物细胞和组织的力学性能、形态发生及生长。细胞壁的微观结构和特性由纤维素微纤丝的取向和力学性能以及细胞壁基质的力学性能所决定。将植物细胞的形状视为一个方棱柱，其轴与扩展和生长的主要方向对齐，已知侧壁（即细胞侧面的细胞壁部分）内微纤丝的取向。然而，对于它们在细胞上下两端的取向却知之甚少。在此，我们通过数值求解线性弹性方程来研究植物细胞壁上下部分内纤维素微纤丝取向的影响。考虑了微纤丝取向的三种不同情形。我们还区分了由垂直于扩展主方向的微纤丝给出的侧壁微观结构以及微纤丝在壁厚方向旋转的情形。利用均匀化理论从细胞壁微纤丝和壁基质弹性特性的微观描述中获得细胞壁的宏观弹性特性。结果发现，细胞壁上下部分微纤丝的取向会影响细胞在横向方向的扩展，并且在作用于植物细胞壁和组织的力的情况下尤为重要。
