Finite element model of polar growth in pollen tubes.

Cellular protuberance formation in walled cells requires the local deformation of the wall and its polar expansion. In many cells, protuberance elongation proceeds by tip growth, a growth mechanism shared by pollen tubes, root hairs, and fungal hyphae. We established a biomechanical model of tip growth in walled cells using the finite element technique. We aimed to identify the requirements for spatial distribution of mechanical properties in the cell wall that would allow the generation of cellular shapes that agree with experimental observations. We based our structural model on the parameterized description of a tip-growing cell that allows the manipulation of cell size, shape, cell wall thickness, and local mechanical properties. The mechanical load was applied in the form of hydrostatic pressure. We used two validation methods to compare different simulations based on cellular shape and the displacement of surface markers. We compared the resulting optimal distribution of cell mechanical properties with the spatial distribution of biochemical cell wall components in pollen tubes and found remarkable agreement between the gradient in mechanical properties and the distribution of deesterified pectin. Use of the finite element method for the modeling of nonuniform growth events in walled cells opens future perspectives for its application to complex cellular morphogenesis in plants.