Dynamic modeling of cell shape during oscillatory pollen tube growth
The pollen tube is a long, thin cell (16 − 20μm diameter, up to 4cm length in lily) that grows out of a pollen grain at germination. In fertilization of flowers, the pollen tube plays a crucial role, creating a path through the stile for the sperm nuclei to reach the egg, deep inside the flower. The driving force for tube growth is turgor pressure, generated by a gradient in solutes across the semipermeable cell membrane. The force of turgor pressure is balanced by the tensile strength of the cell wall. Growth occurs due to localized yielding of the wall. The local rate of expansion is a function of local wall properties and is balanced by secretion (exocytosis) of new wall material so that wall thickness and strength are sustained. Maximum expansion rates are found at the tip of the cell, declining to zero some distance behind the tip  thus leading to growth exclusively at the tip of the cell. The pollen tube cell wall is mainly composed of pectins, polymers of acidic sugars (primarily galacturonic acid) secreted in an esterified form, with a methyl group covalently bound to each acid moiety. Pectin Methylesterase (PME) is secreted with the pectins and over time removes the methyl groups creating negative charges that bind calcium entering from the medium. Once cross-linked, pectins are more resistant to tensile stress in the wall. Wall thickness and local expansion rate are thus determined by the balance between the rate of wall thinning, the rate of deposition of new esterified pectins, and the rate of maturation of the pectins as PME cleaves methoxy groups, and calcium ions form crosslinks. We propose that the regulation of localized deposition and the rate of pectin maturation in the tip region are an important part of the mechanism by which pollen tubes control expansion rates and thus pollen tube polarity and directional growth.
Proceedings of the 5th Mathematics in the Plant Sciences Study Group