title: Hybrid vertex-midline modelling of elongated plant organs.
abstract: 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.
authors.affiliation: Centre for Plant Integrative Biology, School of Biosciences , University of Nottingham , Sutton Bonington LE12 5RD , UK.
authors.forename: John A
authors.identifier: 0000-0001-9181-8083
authors.initials: JA
authors.lastname: Fozard
authors.affiliation: Centre for Plant Integrative Biology, School of Biosciences , University of Nottingham , Sutton Bonington LE12 5RD , UK.
authors.forename: Malcolm J
authors.initials: MJ
authors.lastname: Bennett
authors.affiliation: Centre for Plant Integrative Biology, School of Biosciences, University of Nottingham, Sutton Bonington LE12 5RD, UK; School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
authors.forename: John R
authors.initials: JR
authors.lastname: King
authors.affiliation: School of Mathematics , University of Manchester , Oxford Road, Manchester M13 9PL , UK.
authors.forename: Oliver E
authors.identifier: 0000-0003-0172-6578
authors.initials: OE
authors.lastname: Jensen
keywords: auxin; biomechanics; gravitropism; growth; multicellular; multiscale