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International Conference on Mathematical Biology and

Annual Meeting of The Society for Mathematical Biology,

July 27-30, 2009

University of British Columbia, Vancouver

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Program

MSG1b
Rosemary Dyson
Centre for Plant Integrative Biology, University of Nottingham, UK
Title Mathematical modelling of anisotropic plant root cell growth
Abstract We consider the root elongation zone of the model plant Arabidopsis thaliana, in which cells undergo rapid anisotropic growth: the radius remains approximately constant whilst the length increases 30 fold or more. Plant cells differ from animal cells by the presence of a tough cell wall, containing oriented cellulose microfibrils, which maintains a high turgor pressure within the cell. Growth has been traditionally modelled using the 'Lockhart equation' which relates the growth rate of the cell length to the internal pressure but takes no account of the mechanical anisotropy caused by the microfibrils; growth is assumed to only occur axially.


We employ a fibre-reinforced fluid model for a pressurised hollow viscous cylinder, exploiting the small aspect ratio of the walls, to represent a growing cell. By taking an appropriate limit of the various viscosity functions we give a solution in which the microfibrils maintain the cell radius whilst allowing growth axially. We find an expression for the growth rate of the cell length, which reduces to the 'Lockhart equation' upon appropriate simplification. The model therefore provides insights into the geometric and biomechanical parameters underlying bulk quantities such as 'extensibility', and shows how fibre reorientation may influence growth.
LocationWoodward 1