On the Robustness of the Geometrical Model for Cell Wall Deposition

All plant cells are provided with the necessary rigidity to withstand the turgor by an exterior cell wall. This wall is composed of long crystalline cellulose microfibrils embedded in a matrix of other polysaccharides. The cellulose microfibrils are deposited by mobile membrane bound protein complexes in remarkably ordered lamellar textures. The mechanism by which these ordered textures arise, however, is still under debate. The geometrical model for cell wall deposition proposed by Emons and Mulder (Proc. Natl. Acad. Sci. 95, 7215–7219, 1998) provides a detailed approach to the case of cell wall deposition in non-growing cells, where there is no evidence for the direct influence of other cellular components such as microtubules. The model successfully reproduces even the so-called helicoidal wall; the most intricate texture observed. However, a number of simplifying assumptions were made in the original calculations. The present work addresses the issue of the robustness of the model to relaxation of these assumptions, by considering whether the helicoidal solutions survive when three aspects of the model are varied. These are: (i) the shape of the insertion domain, (ii) the distribution of lifetimes of individual CSCs, and (iii) fluctuations and overcrowding. Although details of the solutions do change, we find that in all cases the overall character of the helicoidal solutions is preserved.