Abstract
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.
Highlights
To better understand plant development, it is important to analyse how the microscopic structure of plant tissues and organs impacts their mechanical properties
A few main results are highlighted by emphazising certain data: (i) italic values contain results representing the main impact of the orientation of the microfibrils in the upper and lower parts of the cell wall; (ii) data in bold highlight the impact of applied forces and of the microstructure in the side walls on the elongation of the cells; (iii) data in bold italic indicate the effect of the microscopic structure on the strain; and (iv) with underline, we mark results that are unique to specific microfibril orientations, boundary conditions and the distribution of cells in the plant tissue
In the case where the microfibrils in the side walls are oriented perpendicular to the cell axis, the presence and orientation of the cellulose microfibrils in the upper and lower parts of the cell wall have little effect on the expansion of the cells in the x3-direction, as can be seen from looking at the columns corresponding to the maximal positive values of the displacement in the x3-direction in Tables 4 and 8
Summary
To better understand plant development, it is important to analyse how the microscopic structure of plant tissues and organs impacts their mechanical properties. In this paper we investigate the impact of the orientation of the cellulose microfibrils in the upper and lower parts of cell walls and of a rotated (plywood-like) distribution of microfibrils in the side walls on the elastic deformation of the plant cell walls and tissues using multiscale modelling and numerical simulations. In the case where the microstructure in the side walls of the cells is defined by layers of microfibrils rotated through the wall thickness, we obtain a much smaller expansion in the direction of the cell’s axis and the orientation of the microfibrils in the upper and lower parts impacts the deformation in the directions orthogonal to the cell’s axis.
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