Abstract
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.
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References
Berleth, T., Scarpella, E., Prusinkiewicz, P., 2007. Towards the systems biology of auxin-transport-mediated patterning. Trends Plant Sci. 12, 151–159.
Brown, R.M. Jr., 1974. The Golgi apparatus and endomembrane system; its role in the biosynthesis, transport, and secretion of cell wall constituents in Pleurochrysis. In: Prais, H.S. (Ed.), International Symposium on Plant Cell Differentiation. Lisbon, Portugal, August 1974. Port. Acta Biol. 14, 369–384.
Brown, R.M. Jr., 1979. Biogenesis of natural polymer systems, with special reference to cellulose assembly and deposition. In: Proceedings of the Third Phillip Morris U.S.A. Operations Center. Richmond, Virginia, November 1978, pp. 50–123.
Brown, R.M. Jr., Montezinos, D., 1976. Cellulose microfibrils: visualization of biosynthetic and orienting complexes in association with the plasma membrane. Proc. Natl. Acad. Sci. USA 73, 143–147.
Brown, R.M. Jr., Romanovicz, D.K., 1976. Biogenesis and structure of Golgi-derived cellulosic scales in Pleurochrysis. I. Role of the endomembrane system in scale assembly and exocytosis. Appl. Polym. Symp. 28, 537–585.
Carpita, N.C., Gibeaut, D.M., 1993. Structural models of primary cell walls in flowering plants: consistency of molecular structure with the physical properties of the walls during growth. Plant J. 3, 1–30.
De Ruijter, N.C.A., Rook, M.B., Bisseling, T., Emons, A.M.C., 1999. Lipochito-oligosaccharides re-initiate root hair tip growth in vicia sativa with high calcium and spectrin-like antigen at the tip. Plant J. 13, 341–350.
Diotallevi, F., 2007. The physics of cellulose biosynthesis: polymerization and self-organization from plants to bacteria. PhD thesis, Wageningen University. Downloadable from: http://www.amolf.nl/publications/theses/diotallevi/diotallevi.html.
Diotallevi, F., Mulder, B., 2007. The cellulose synthase complex: a polymerization driven supramolecular motor. Biophys. J. 92, 2666–2673.
Emons, A.M.C., 1985. Plasma membrane rosettes in root hairs of Equisetum Hyemale. Planta 163, 350–359.
Emons, A.M.C., 1988. Methods for visualizing cell wall texture. Acta Bot. Neerl. 37, 31–38.
Emons, A.M.C., 1994. Winding threads around plant cells: a geometrical model for microfibril deposition. Plant Cell Environ. 17, 3–14.
Emons, A.M.C., Mulder, B.M., 1997. Plant cell wall architecture. Commun. Theor. Biol. 4, 115–131.
Emons, A.M.C., Mulder, B.M., 1998. The making of the architecture of the plant cell wall: how cells exploit geometry. Proc. Natl. Acad. Sci. 95, 7215–7219.
Emons, A.M.C., Wolters-Arts, A.M.C., 1983. Cortical microtubules and microfibril deposition in the cell wall of root hairs of Equisetum Hyemale. Protoplasma 117, 68–81.
Emons, A.M.C., Derksen, J., Sassen, M.M.A., 1992. Do microtubules orient plant cell wall microfibrils? Physiol. Plant. 84, 486–493.
Giddings, T.H., Staehelin, L.A., 1991. Microtubule-mediated control of microfibril deposition: a reexamination of the hypothesis. In: Lloyd, C.W. (Ed.), The Cytoskeletal Basis of Plant Growth and Form, pp. 85–99. Academic Press, San Diego.
Herth, W., 1980. Calcofluor white and Congo red inhibit chitin microfibril assembly of poterioochromonas: evidence for a gap between polymerization and microfibril formation. J. Cell Biol. 87, 442–450.
Himmelspach, R., Williamson, R.E., Wasteneys, G.O., 2003. Cellulose microfibril alignment recovers from DCB-induced disruption despite microtubule disorganization. Plant J. 36, 565–575.
Krakauer, D.C., 2004. Robustness in Biological Systems: a provisional taxonomy. In: Deisboeck, T.S., Kresh, J.Y. (Eds.), Complex Systems Science in Biomedicine. Kluwer/Springer, New York.
Mueller, S.C., Brown, R.M. Jr., 1980. Evidence for an intramembranous component associated with a cellulose microfibril synthesizing complex in higher plants. J. Cell Biol. 84, 315–326.
Mulder, B.M., Emons, A.M.C., 2001. A dynamical model for plant cell wall deposition. J. Math. Biol. 42, 261–289.
Neville, A.C., 1993. Biology of Fibrous Composites: Development Beyond the Cell Membrane. Cambridge University Press, Cambridge.
Paredez, A.R., Sommerville, C.R., Ehrhardt, D.W., 2006. Visualization of cellulose synthase demonstrates functional association with microtubules. Science 312, 1491–1495.
Petty, H.R., Worth, R.G., Kindzelskii, A.L., 2000. Imaging sustained dissipative patterns in the metabolism of individual living cells. Phys. Rev. Lett. 84, 2754–2757.
Roberts, K., 1989. The plant extracellular matrix. Curr. Opin. Cell Biol. 5, 1020–1027.
Roland, J.-C., Vian, B., Reis, D., 1977. Further observations on cell wall morphogenesis and polysaccheride arrangement during plant growth. Protoplasma 91, 125–141.
Saxena, I.M., Brown, R.M. Jr., Kudlicka, K., 1996. Cellulose biosynthesis in higher plants. Trends Plant Sci. 1, 149–156.
Shimmen, T., 2007. The sliding theory of cytoplasmic streaming: fifty years of progress. J. Plant Res. 120, 31–43.
Sommerville, C.R., 2006. Cellulose synthesis in higher plants. Ann. Rev. Cell Dev. Biol. 22, 53–78.
Willison, J.H.M., Brown, R.M. Jr., 1978a. A model for the pattern of microfibrils in the cell wall of Glaucocystis. Planta 141, 51–58.
Willison, J.H.M., Brown, R.M. Jr., 1978b. Cell wall structure and deposition in Glaucocystis. J. Cell Biol. 77, 103–119.
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Diotallevi, F., Mulder, B.M. & Grasman, J. On the Robustness of the Geometrical Model for Cell Wall Deposition. Bull. Math. Biol. 72, 869–895 (2010). https://doi.org/10.1007/s11538-009-9472-0
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DOI: https://doi.org/10.1007/s11538-009-9472-0