Expansive growth is a process by which walled cells of 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 perform multiple functions simultaneously, including providing structural support by combining elastic and irreversible deformation and facilitating the deposition of new material during growth. This is accomplished by a network of microfibrils and tethers composed of complex polysaccharides and proteins that can dynamically mediate the network topology via periodic detachment and reattachment events. Lockhart and Ortega have provided crucial macroscopic understanding of the expansive growth process through global biophysical models, but these models lack the connection to molecular processes that trigger network rearrangements in the wall. Interestingly, the helical growth of the fungal sporangiophores of Phycomyces blakesleeanus is attributed to a limited region (called the growth zone) where microfibrils are deposited, followed by reorientation and slip. Based on past evidence of dominant shear strain between microfibrils (slippage), we propose a mechanistic model of a network of sliding fibrils connected by tethers. A statistical approach is introduced to describe the population behavior of tethers that have elastic properties and the ability to break and reform in time. These properties are responsible for global cell wall mechanics such as creep and stress relaxation. Model predictions are compared with experiments from literature on stress relaxation and turgor pressure step up for the growing cells of P. blakesleeanus, which are later extended to incised pea (Pisum sativus L.) and the algae Chara corallina using the unique dimensionless number Πpe for 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 provides critical insights on cell wall dynamics at a molecular level.
