A Statistical Model of Cell Wall Dynamics during Expansive Growth

Abstract

Expansive growth is a process by which walled cells found in plants, algae and fungi, use turgor pressure to mediate irreversible wall deformation and regulate their shape and volume. The molecular structure of the primary cell wall must therefore be able to perform multiple function simultaneously such as providing structural support by a combining elastic and irreversible deformation and facilitate the deposition of new material during growth. This is accomplished by a network of microfibrils and tethers composed of complex polysaccharides and proteins that are able to dynamically mediate the network topology via constant detachment and reattachment events. Global biophysical models such as those of Lockhart and Ortega have provided crucial macroscopic understanding of the expansive growth process, but they lack the connection to molecular processes that trigger network rearrangements in the wall. In this context, we propose a statistical approach that describes the population behavior of tethers that have elastic properties and the ability to break and re-form in time. Tether properties such as bond lifetimes and stiffness, are then shown to govern global cell wall mechanics such as creep and stress relaxation. The model predictions are compared with experiments of stress relaxation and turgor pressure step-up from existing literature, for the growing cells of incised pea (Pisum sativus L.), algae Chara corallina and the sporangiophores of the fungus, Phycomyces blakesleeanus. The molecular parameters are estimated from fits to experimental measurements combined with the information on the dimensionless number {Pi}pe that is unique to each species. To our knowledge, this research is the first attempt to use a statistical approach to model the cell wall during expansive growth and we believe it will provide a better understanding of the cell wall dynamics at a molecular level.