Modelling Plant Cell Growth


Plants are sessile organisms and they must adapt their growth to a changing environment. Understanding plant growth requires to study the interplay of turgor, cellular hydrodynamics, mechanical properties of cell walls and addition of materials to cell walls, as well as the actions of phytohormones. Mathematical modelling is a useful tool for tackling the complexity in plant growth. The scope of this article is to discuss the fundamental aspects of modelling plant cell growth. In order for a plant cell to grow, the cell wall must expand, water must enter the cell and turgor pressure must be able to provide mechanical support. During cell growth, the relative change in the water volume and the relative change in cell wall chamber volume are approximately equal. Mathematical equations for modelling plant cell growth are described to establish how cell volume and turgor can be calculated. Mathematical equations for ion transport are introduced to establish how osmotic pressure can be calculated. Combination of those equations formulates a method for modelling plant cell growth. Modelling of auxin dynamics, which play a key role in controlling cell expansion, is also described. One of the future challenges is to model the interplay between plant growth and auxin dynamics.

Key Concepts

  • The plant cell is surrounded by the cell wall.
  • In order for a plant cell to grow, the cell wall must expand, water must enter the cell and turgor pressure must be able to provide mechanical support.
  • Turgor and cell volume are calculated using the mathematical equations, which describe that the relative change in the water volume and the relative change in cell wall chamber volume are approximately equal during the cell growth.
  • Cellular ion concentrations and osmotic pressure are calculated using the equations that describe reversal potentials and voltage gating.
  • The phytohormone auxin plays an essential role in many aspects of plant growth and development.
  • Auxin concentration in the cells is a function of multiple factors including biosynthesis, degradation and conjugation, and transport.
  • Modelling auxin dynamics needs to appropriately formulate the equations including auxin biosynthesis, degradation and transport.
  • To model the role of auxin in plant cell growth, it is necessary to establish how auxin is related to the key factors for plant cell growth including turgor, cellular hydrodynamics, mechanical properties of cell wall materials and addition of materials to the cell wall.

Keywords: plant growth; mathematical modelling; turgor; cell wall; cellular osmotic pressure; ions; ion transport; modelling auxin dynamics

Figure 1. A schematic description about modelling plant cell growth. This figure shows how the key factors including water volume, cell wall chamber volume, turgor, cell wall properties and addition of materials to cell wall, as well as cellular and extracellular osmotic pressure, are related during cell growth. Equations in the text establish how these factors are quantitatively connected with each other during cell growth.
Figure 2. A schematic description about modelling the interplay between plant growth and auxin dynamics. This figure shows how eqns can be coupled with eqn .


Adamowski M and Friml J (2015) PIN‐dependent auxin transport: action, regulation, and evolution. Plant Cell 27: 20–32.

Band LR, Wells DM, Fozard JA, et al. (2014) Systems analysis of auxin transport in the Arabidopsis root apex. Plant Cell 26: 862–875.

Bennett T, Hines G, van Rongen M, et al. (2016) Connective auxin transport in the shoot facilitates communication between shoot apices. PLoS Biology 14: e1002446.

Braybrook SA and Peaucelle A (2013) Mechano‐chemical aspects of organ formation in Arabidopsis thaliana: the relationship between auxin and pectin. PLoS One 8: e57813.

Brunoud G, Wells DM, Oliva M, et al. (2012) A novel sensor to map auxin response and distribution at high spatio‐temporal resolution. Nature 482: 103–106.

Chebli Y and Geitmann A (2017) Cellular growth in plants requires regulation of cell wall biochemistry. Current Opinion in Cell Biology 44: 28–35.

Cho M and Cho HT (2012) The function of ABCB transporters in auxin transport. Plant Signaling & Behavior 8: e22990.

Cleland RE (1984) The Instron technique as a measure of immediate‐past wall extensibility. Planta 160: 514–520.

Cosgrove DJ (2005) Growth of the plant cell wall. Nature Reviews. Molecular Cell Biology 6: 850–861.

Cosgrove DJ (2016) Plant cell wall extensibility: connecting plant cell growth with cell wall structure, mechanics, and the action of wall modifying enzymes. Journal of Experimental Botany 67: 463–476.

Eggen E, de Keijser MN and Mulder BM (2011) Self‐regulation in tip growth: the role of cell wall ageing. Journal of Theoretical Biology 283: c113–c121.

Friml J, Benkova E, Blilou I et al. (2002) AtPIN4 mediates sink‐driven auxin gradients and root patterning in Arabidopsis. Cell 108: 661–673.

Gradmann D (2001) Models for oscillations in plants. Australian Journal of Plant Physiology 28: 577–590.

Grieneisen VA, Xu J, Maree AFM, Hogeweg P and Scheres B (2007) Auxin transport is sufficient to generate a maximum and gradient guiding root growth. Nature 449: 1008–1013.

Grieneisen VA, Scheres B, Hogeweg P and M Marée AF (2012) Morphogengineering roots: comparing mechanisms of morphogen gradient formation. BMC Systems Biology 6: 37.

Hill AE, Shachar‐Hill B, Skepper JN, Powell J and Shachar‐Hill Y (2012) An osmotic model of the growing pollen tube. PLoS One 7: e36585.

Kato N, He H and Steger AP (2010) A systems model of vesicle trafficking in Arabidopsis pollen tubes. Plant Physiology 152: 590–601.

Kroeger J, Zerzour R and Geitmann A (2011) Regulator or driving force? The role of turgor pressure in oscillatory plant cell growth. PLoS One 6: e18549.

Liao CY, Smet W, Brunoud G, et al. (2015) Reporters for sensitive and quantitative measurement of auxin response. Nature Methods 12: 207–210.

Liu JL, Mehdi S, Topping J, Tarkowski P and Lindsey K (2010a) Modelling and experimental analysis of hormonal crosstalk in Arabidopsis. Molecular Systems Biology 6: 373.

Liu J, Piette BMAG, Deeks MJ, Franklin‐Tong VE and Hussey PJ (2010b) A compartmental model analysis of integrative and self‐regulatory ion dynamics in pollen tube growth. PLoS One 5: e13157.

Liu JL, Grieson CS, Webb AAR and Hussey PJ (2010c) Modelling dynamic plant cells. Current Opinion in Plant Biology 13: 744–749.

Liu J and Hussey PJ (2011) Towards the creation of a systems tip growth model for a pollen tube. Plant Signaling & Behavior 6: 520–522.

Liu JL, Mehdi S, Topping J, Friml J and Lindsey K (2013) Interaction of PLS and PIN and hormonal crosstalk in Arabidopsis root development. Frontiers in Plant Science 4: 75.

Liu J and Hussey PJ (2014) Dissecting the regulation of pollen tube growth by modeling the interplay of hydrodynamics, cell wall and ion dynamics. Frontiers in Plant Science 5: 392.

Liu J, Rowe J and Lindsey K (2014) Hormonal crosstalk for root development: a combined experimental and modeling perspective. Frontiers in Plant Science 5: 116.

Ljung K (2013) Auxin metabolism and homeostasis during plant development. Development 140: 943–950.

Lockhart JA (1965) An analysis of irreversible plant cell elongation. Journal of Theoretical Biology 8: 264–275.

Ludwig‐Müller J (2011) Auxin conjugates: their role for plant development and in the evolution of land plants. Journal of Experimental Botany 62: 1757–1773.

Mellor N, Adibi M, El‐Showk S, et al. (2017) Theoretical approaches to understanding root vascular patterning: a consensus between recent models. Journal of Experimental Botany 68: 5–16.

Moore S, Zhang X, Liu J and Lindsey K (2015a) Some fundamental aspects of modelling auxin patterning in the context of auxin‐ethylene‐cytokinin crosstalk. Plant Signaling & Behavior 10: e1056424.

Moore S, Zhang X, Mudge A, et al. (2015b) Spatiotemporal modelling of hormonal crosstalk explains the level and patterning of hormones and gene expression in Arabidopsis thaliana wildtype and mutant roots. New Phytologist 207: 1110–1122.

Moore S, Liu J, Zhang X and Lindsey K (2017) A recovery principle provides insight into auxin pattern control in the Arabidopsis root. Scientific Reports 7: 430004.

Ortega JKE (2010) Plant cell growth in tissue. Plant Physiology 154: 1244–1253.

Ortega JKE and Welch SWJ (2013) Mathematical models for expansive growth of cells with walls. Mathematical Modelling of Natural Phenomena 8: 35–61.

Petersson SV, Johansson AI, Kowalczyk M, et al. (2009) An auxin gradient and maximum in the Arabidopsis root apex shown by high‐resolution cell‐specific analysis of IAA distribution and synthesis. Plant Cell 21: 1659–1668.

Rojas E, Hotton S and Dumais J (2011) Chemically mediated mechanical expansion of the pollen tube cell wall. Biophysical Journal 101: 1844–1853.

Sabatini S, Beis D, Wolkenfelt H, et al. (1999) An auxin‐dependent distal organizer of pattern and polarity in the Arabidopsis root. Cell 99: 463–472.

Swarup R and Peret B (2012) AUX/LAX family of auxin influx carriers‐an overview. Frontiers in Plant Science 3: 225.

Ulmasov T, Murfett J, Hagen G and Guilfoyle TJ (1997) Aux/IAA proteins repress expression of reporter genes containing natural and highly active synthetic auxin response elements. The Plant Cell 9: 1963–1971.

Vanneste S and Friml J (2009) Auxin: a trigger for change in plant development. Cell 136: 1005–1016.

von Wangenheim D, Fangerau J, Schmitz A, et al. (2016) Rules and self‐organizing properties of postembryonic plant organ cell Division Patterns. Current Biology 26: 439–449.

Winship LJ, Obermeyer G, Geitmann A and Hepler PK (2011) Pollen tubes and the physical world. Trends in Plant Science 16: 353–355.

Yan A, Xu G and Yang Z‐B (2009) Calcium participates in feedback regulation of the oscillating ROP1 Rho GTPase in pollen tubes. Proceedings of the National Academy of Sciences of the United States of America 106: 22002–22007.

Yoshida S, Barbier de Reuille P, Lane B, et al. (2014) Genetic control of plant development by overriding a geometric division rule. Developmental Cell 29: 75–87.

Zazimalova E, Murphy AS, Yang H, Hoyerova K and Hosek P (2010) Auxin transporters – why so many? Cold Spring Harbor Perspectives in Biology 2: a001552.

Zhao Y (2010) Auxin biosynthesis and its role in plant development. Annual Review of Plant Biology 61: 49–64.

Zonia L and Munnik T (2011) Understanding pollen tube growth: the hydrodynamic model versus the cell wall model. Trends in Plant Science 16: 347–352.

Further Reading

Kariyan J, Konforti B and Wemmer D (2013) The Molecules of Life: Physical and Chemical Principles. New York: Garland Science, Taylor & Francis Group.

Murray JD (2003a) Mathematical Biology: I: Introduction. Berlin: Springer‐Verlag.

Murray JD (2003b) Mathematical Biology: II: Spatial Models and Biomedical Applications. Berlin: Springer‐Verlag.

Taiz L and Zeiger E (2010) Plant Physiology, 5th edn. Sunderland, MA: Sinauer Associates.

Contact Editor close
Submit a note to the editor about this article by filling in the form below.

* Required Field

How to Cite close
Liu, Junli, Moore, Simon, and Lindsey, Keith(Nov 2017) Modelling Plant Cell Growth. In: eLS. John Wiley & Sons Ltd, Chichester. [doi: 10.1002/9780470015902.a0020107.pub2]