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.     

The Teorell membrane oscillator as a mechano-electric transducer

Summary The results of a recent quantitative analysis of the Teorell membrane oscillator are utilized to explore its role as an excitability analogue. Special attention is paid to its role as a mechano-electric transducer. A membrane of exceptionally well-defined pore structure has been used in this study. The analogue properties arise from nonlinear coupling between water and salt fluxes. When the membrane is simultaneously subjected to controlled gradients of hydrostatic pressure, electrical potential and concentration, bi-stable stationary states can be produced. These arise from the opposing effects of pressure and electro-osmosis on the volume flow. Transitions between these states show hysteresis. The factors governing such transitions are analogous to certain types of stimuli encountered in the natural excitation process. The membrane system also shows oscillatory behavior when the hydrostatic pressure gradient is allowed to vary under constant current conditions. This property is related to the bi-stable stationary state phenomena and is compared to the regenerative behavior found in biologically excitable tissues. Particular emphasis is placed upon analogies between the membrane oscillator and certain natural tissues. The importance of the nonlinear nature of the force-flux coupling in the analogue is stressed, and its possible relevance to biological excitability indicated. Some consideration is also given to the role of electro-osmotic flux coupling in biological tissues.