| The growth of walled cells is due to the cooperation of physical and chemical mechanisms leading to the controlled mechanical deformation of the cells. Plant cells, for example, need to expand the surface area of their cell wall in order to grow in size. This can be done in a uniform manner called diffusive growth or through tip-growth. Tip-growth is characterised by a mechanical deformation that is confined to a specific region of the cell wall, namely its tip. Tip-growth generally leads to tubular cell wall shapes and has been observed in plant cells such as pollen tubes and root hairs but also in fungal hyphae, algae and neuronal growth cones. The pollen tube is a protuberance growing on the pollen grain. As part of plant fertilisation, its purpose is to extend until it reaches the ovule of a host plant and allow for the passage of a sperm cell contained in the pollen grain.A very intriguing phenomenon, observed a decade ago, concerning growing pollen tubes is the oscillation in time of the growth rate, the concentration of signalling molecules such as calcium and the thickness of the cell wall. While the total interaction of the components of such a complex system is hard to asses, I show that a few key elements, when coupled adequately, lead to the steady oscillation similar to that observed experimentally. The growing cell was modelled as a fluid finger in the viscous regime with elastic properties depending on the material delivery to the growing region. The difference between the material delivered and the material required for growth led to the stable oscillation of the growth rate. A second phenomenon common to all pollen tubes is a bidirectional cytoplasmic flow, generated by the movement of individual organelles along the cytoskeletal arrays. One important purpose is the transport to the apex of polysaccharides, phospholipids and proteins necessary for the assembly of the elongating tube. This material flow and its effect on actin polymerisation is modelled, indirectly predicting a shape for the spatial profile of the actin array. The profile resulting from the model as well as the patterns of vesicle flux and distribution match experimental data. Finally, the flow of lipids during the rupture of charged biological membranes is studied. An explanation is proposed for the difference of two orders of magnitude between the observed flow velocity and the one predicted by the prevailing theory. In order to take into account the effect of water friction on the lipid flow, the flow equations must be treated in the viscous regime and not in the inertial regime. This analysis leads to a rupture velocity within the range measured experimentally.This thesis studies how physical principles direct and control the tip-growth of a pollen tube. The three particular phenomena that were addressed concern the effects of elastic forces and short-range electrical potentials on ion diffusion, actin protein aggregation and the viscous flow in growing pollen tubes. |
