## Modelling Plant Cell Growth

### Abstract

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 .

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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.

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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.

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