Hybrid vertex-midline modelling of elongated plant organs
Fozard, John A. and Bennett, Malcolm J. and King, John R. and Jensen, Oliver E. (2016) Hybrid vertex-midline modelling of elongated plant organs. Interface Focus, 6 (4). 20160043/1-20160043/14. ISSN 2042-8901
We describe a method for the simulation of the growth of elongated plant organs, such as seedling roots. By combining a midline representation of the organ on a tissue scale and a vertex-based representation on the cell scale, we obtain a multiscale method, which is able to both simulate organ growth and incorporate cell-scale processes. Equations for the evolution of the midline are obtained, which depend on the cell-wall properties of individual cells through appropriate averages over the vertex-based representation. The evolution of the organ midline is used to deform the cellular-scale representation. This permits the investigation of the regulation of organ growth through the cell-scale transport of the plant hormone auxin. The utility of this method is demonstrated in simulating the early stages of the response of a root to gravity, using a vertex-based template acquired from confocal imaging. Asymmetries in the concentrations of auxin between the upper and lower sides of the root lead to bending of the root midline, reflecting a gravitropic response.
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