A mathematical model of the diffuse growth of the primary wall of plant cells
DOI:
https://doi.org/10.32480/rscp.2018-23-1.13-34Keywords:
mathematical models, diffuse plant cell growth, Lockhart model, augmented growth equation, mechanical models of primary cell wall, orthotropy and plasticity of cellular wallAbstract
A mathematical model is constructed to study the diffuse axial and radial growth of the primary wall of plant cells. Analytical formulas are obtained for Erickson's anisotropy quotient of growth and for the parameters of the Ortega ?s augmented equation, as a function of the parameters of the new model. A non-linear constitutive relationship is introduced in the Lockhart model and some aspects of the axial growth model thus generalized are considered.
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References
1. Noble PS. Physicochemical and Environmental Plant Physiology, 4th edition. Amsterdam: Elsevier, 2009.
2. Taiz L, Zeiger E, Moller IM, Murphy A. Plant Physiology and Development, 6th edition. New York: Oxford University Press, 2014.
3. Taiz L, Zeiger E, Moller IM, Murphy A. Fundamentals of Plant Physiology. New York: Oxford University Press, 2018.
4. Burgert I, Dunlop JW. Micromechanics of cell walls. En: Wojtaszek P, editor. Mechanical Integration of Plant Cells and Plants. Signaling and Communication. In Plants. Berlin: Springer, 2011, pp. 27-52.
5. Cosgrove D. Growth of the plant cell wall, Nature Reviews. Molecular Cell Biology. 2005;6:850-861.
6. Baskin TI. Anisotropic Expansion of the Plant Cell Wall. Annual Reviews of Cell and Developmental Biology. 2005;21:203–22.
7. Gibson LJ. The hierarchical structure and mechanics of plant materials. Journal of the Royal Society Interface. 2012;9:2749-2766.
8. Erickson RO. Microfibrillar structure of growing plant cell walls. En Getz, WM, editor. Mathematical Modeling in Biology and Ecology, Lecture Notes. In Biomathematics, vol. 33. Berlin: Springer 1980, pp. 192-212
9. Lockhart JA. An analysis of irreversible plant cell elongation. Journal of Theoretical Biology. 1965;8:264-275.
10. Suárez Antola R. Una clase de modelos matemáticos que describen el alargamiento irreversible de células vegetales: análisis de sus propiedades genéricas mediante la teoría de las perturbaciones singulares. En II Congreso Internacional de Biomatemática. Buenos Aires, Argentina, 1984.
11. Suárez Antola R, Rodríguez Bogorja F. Análisis del módulo de Young en la pared primaria de la célula vegetal. Montevideo: Universidad de la República, 1984.
12. Suárez Antola R. Elasticidad, plasticidad y flujo de volumen en las células vegetales. Montevideo: Universidad de la República, 1985.
13. Ortega JK. Augmented growth equation for cell wall expansion. Plant Physiology. 1985;79:318-320.
14. Ortega JK. Plant cell growth in tissue. Plant Physiology. 2010;154:1244-1253.
15. Proseus TE, Ortega JK. Separating growth from elastic deformation during cell enlargement. Plant Physiology. 1999;119:775-784.
16. Pietruszka M. Solution for a local equation of anisotropic plant growth: an analytical study of expansin activity. Journal of the Royal Society Interface. 2011;8:975-987.
17. Huang R, Becker AA, Jones IA. Modeling cell wall growth using a fiber reinforced hyper- elastic constitutive law. Journal of the Mechanics and Physics of Solids. 2012;60:750-783.
18. Veytsman BA, Cosgrove D. A model of cell wall expansion based on thermodynamics of polymer networks. Biophysical Journal. 1998;75:2240-2250.
19. Frey-Wyssling A. Deformation and Flow in Biological Systems. New York: Interscience, 1952.
20. Katchalsky A. Curran F. Nonequilibrium Thermodynamics in Biophysics. Cambridge MA: Harvard University Press, 1967.
21. Ortega JK. Dimensionless number is central to stress relaxation and expansive growth of the cell wall. Nature Scientific Reports. 2017;7:3016. doi:10.1038/s41598-017-03002-6
22. Cosgrove D. Plant cell wall extensibility: connecting plant cell growth with cell wall structure, mechanics, and the action of wall modifying enzymes. Journal of Experimental Botany. 2016;67(2): 463–476.
23. Cosgrove D. Diffuse Growth of Plant Cell Walls. Plant Physiology. 2018;176:16-27.
24. Bruce D. Mathematical modelling of the cellular mechanics of plant. Philosophical Transactions of the Royal Society (London) B. 2003;358:1437–1444.
2. Taiz L, Zeiger E, Moller IM, Murphy A. Plant Physiology and Development, 6th edition. New York: Oxford University Press, 2014.
3. Taiz L, Zeiger E, Moller IM, Murphy A. Fundamentals of Plant Physiology. New York: Oxford University Press, 2018.
4. Burgert I, Dunlop JW. Micromechanics of cell walls. En: Wojtaszek P, editor. Mechanical Integration of Plant Cells and Plants. Signaling and Communication. In Plants. Berlin: Springer, 2011, pp. 27-52.
5. Cosgrove D. Growth of the plant cell wall, Nature Reviews. Molecular Cell Biology. 2005;6:850-861.
6. Baskin TI. Anisotropic Expansion of the Plant Cell Wall. Annual Reviews of Cell and Developmental Biology. 2005;21:203–22.
7. Gibson LJ. The hierarchical structure and mechanics of plant materials. Journal of the Royal Society Interface. 2012;9:2749-2766.
8. Erickson RO. Microfibrillar structure of growing plant cell walls. En Getz, WM, editor. Mathematical Modeling in Biology and Ecology, Lecture Notes. In Biomathematics, vol. 33. Berlin: Springer 1980, pp. 192-212
9. Lockhart JA. An analysis of irreversible plant cell elongation. Journal of Theoretical Biology. 1965;8:264-275.
10. Suárez Antola R. Una clase de modelos matemáticos que describen el alargamiento irreversible de células vegetales: análisis de sus propiedades genéricas mediante la teoría de las perturbaciones singulares. En II Congreso Internacional de Biomatemática. Buenos Aires, Argentina, 1984.
11. Suárez Antola R, Rodríguez Bogorja F. Análisis del módulo de Young en la pared primaria de la célula vegetal. Montevideo: Universidad de la República, 1984.
12. Suárez Antola R. Elasticidad, plasticidad y flujo de volumen en las células vegetales. Montevideo: Universidad de la República, 1985.
13. Ortega JK. Augmented growth equation for cell wall expansion. Plant Physiology. 1985;79:318-320.
14. Ortega JK. Plant cell growth in tissue. Plant Physiology. 2010;154:1244-1253.
15. Proseus TE, Ortega JK. Separating growth from elastic deformation during cell enlargement. Plant Physiology. 1999;119:775-784.
16. Pietruszka M. Solution for a local equation of anisotropic plant growth: an analytical study of expansin activity. Journal of the Royal Society Interface. 2011;8:975-987.
17. Huang R, Becker AA, Jones IA. Modeling cell wall growth using a fiber reinforced hyper- elastic constitutive law. Journal of the Mechanics and Physics of Solids. 2012;60:750-783.
18. Veytsman BA, Cosgrove D. A model of cell wall expansion based on thermodynamics of polymer networks. Biophysical Journal. 1998;75:2240-2250.
19. Frey-Wyssling A. Deformation and Flow in Biological Systems. New York: Interscience, 1952.
20. Katchalsky A. Curran F. Nonequilibrium Thermodynamics in Biophysics. Cambridge MA: Harvard University Press, 1967.
21. Ortega JK. Dimensionless number is central to stress relaxation and expansive growth of the cell wall. Nature Scientific Reports. 2017;7:3016. doi:10.1038/s41598-017-03002-6
22. Cosgrove D. Plant cell wall extensibility: connecting plant cell growth with cell wall structure, mechanics, and the action of wall modifying enzymes. Journal of Experimental Botany. 2016;67(2): 463–476.
23. Cosgrove D. Diffuse Growth of Plant Cell Walls. Plant Physiology. 2018;176:16-27.
24. Bruce D. Mathematical modelling of the cellular mechanics of plant. Philosophical Transactions of the Royal Society (London) B. 2003;358:1437–1444.
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2018-10-13
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1.
A mathematical model of the diffuse growth of the primary wall of plant cells. Rev. Soc. cient. Py. [Internet]. 2018 Oct. 13 [cited 2025 Sep. 24];23(1):13-34. Available from: https://sociedadcientifica.org.py/ojs/index.php/rscpy/article/view/33
