Finite Element Model of Polar Growth in Pollen Tubes  

Abstract

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.

Self-regulation in tip-growth: The role of cell wall ageing

“…Zerzour et al, 2009) and biochemical (see e.g. Fayant et al, 2010) measurements that probe the local properties of the wall with quantitative measurement on the local rate of exocytosis (see e.g. Zonia and Munnik, 2008) may serve to validate some of the ideas presented here.…”

“…To give a realistic account of the full growth dynamics clearly requires considering the mechanical properties of the cell wall, which currently is an active area of research (see e.g. Goriely and Tabor (2003a); Dumais et al (2006); Campàs and Mahadevan (2009);Fayant et al (2010)). However, this is beyond the scope of the current work, which focusses on the generic aspects of wall ageing on the overall expansion rate.…”

“…If we now assume that to a first approximation the incorporation rate is proportional to the local calcium concentration, itself taken to be proportional to the ion-channel density, and that the active channels have an exponentially distributed lifetime, we have a first example of such a Poissonian ageing process. Another example is the increasing stiffening of the cell wall due to the ongoing de-esterification of pectins under the action of co-deposited pectin methylesterases (Fayant et al, 2010). If these enzymes are present in abundance, and the rate of cleavage per methyl group is constant, one expects an exponential decay of the number of uncleaved methyl groups per amount of pectin as a function of time after insertion.…”

“…He argued that the newly delivered material right at the tip should be easily deformable to allow for extensional growth, while the material farther from the tip should effectively rigidify to resist further expansion in the radial direction. Indeed, over the past few years a number of papers have appeared that recognize that a proper mechanical description of growth must involve the notion of a gradient in material properties over the apical region (Goriely and Tabor, 2003a,b;Dumais et al, 2006;Fayant et al, 2010). In these approaches, however, this gradient is at the outset chosen to have a fixed, usually phenomenologically motivated, functional form.…”

PECTIN METHYLESTERASE48 Is Involved in Arabidopsis Pollen Grain Germination

“…Despite the importance of this crucial step that leads to seed production, the molecular mechanisms implicated in the spatial and temporal controls of pollen tube growth are not fully known (Johnson and Lord, 2006;Palanivelu and Tsukamoto, 2012). However, it has been proposed that the modulation of the stiffness of the pollen tube was important during pollen tube growth (Parre and Geitmann, 2005a;Fayant et al, 2010;Vogler et al, 2013). Pollen tube elongation is highly polarized, with the growth area being restricted to the apex of the tube.…”