title: Mechanical modelling quantifies the functional importance of outer tissue layers during root elongation and bending.
abstract: Root elongation and bending require the coordinated expansion of multiple cells of different types. These processes are regulated by the action of hormones that can target distinct cell layers. We use a mathematical model to characterise the influence of the biomechanical properties of individual cell walls on the properties of the whole tissue. Taking a simple constitutive model at the cell scale which characterises cell walls via yield and extensibility parameters, we derive the analogous tissue-level model to describe elongation and bending. To accurately parameterise the model, we take detailed measurements of cell turgor, cell geometries and wall thicknesses. The model demonstrates how cell properties and shapes contribute to tissue-level extensibility and yield. Exploiting the highly organised structure of the elongation zone (EZ) of the Arabidopsis root, we quantify the contributions of different cell layers, using the measured parameters. We show how distributions of material and geometric properties across the root cross-section contribute to the generation of curvature, and relate the angle of a gravitropic bend to the magnitude and duration of asymmetric wall softening. We quantify the geometric factors which lead to the predominant contribution of the outer cell files in driving root elongation and bending.
authors.affiliation: School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK.
authors.forename: Rosemary J
authors.initials: RJ
authors.lastname: Dyson
authors.affiliation: Centre for Ultrastructural Imaging, King's College London, London, SE1 1UL, UK.
authors.forename: Gema
authors.initials: G
authors.lastname: Vizcay-Barrena
authors.affiliation: Centre for Plant Integrative Biology, University of Nottingham, Sutton Bonington, LE12 5RD, UK.
authors.forename: Leah R
authors.initials: LR
authors.lastname: Band
authors.affiliation: School of Physics & Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
authors.forename: Anwesha N
authors.initials: AN
authors.lastname: Fernandes
authors.affiliation: Centre for Plant Integrative Biology, University of Nottingham, Sutton Bonington, LE12 5RD, UK.
authors.forename: Andrew P
authors.initials: AP
authors.lastname: French
authors.affiliation: Centre for Plant Integrative Biology, University of Nottingham, Sutton Bonington, LE12 5RD, UK.
authors.forename: John A
authors.initials: JA
authors.lastname: Fozard
authors.affiliation: Centre for Plant Integrative Biology, University of Nottingham, Sutton Bonington, LE12 5RD, UK.
authors.forename: T Charlie
authors.initials: TC
authors.lastname: Hodgman
authors.affiliation: Centre for Plant Integrative Biology, University of Nottingham, Sutton Bonington, LE12 5RD, UK.
authors.forename: Kim
authors.initials: K
authors.lastname: Kenobi
authors.affiliation: School of Computer Science, University of Nottingham, Jubilee Campus, Nottingham, NG8 1BB, UK.
authors.forename: Tony P
authors.initials: TP
authors.lastname: Pridmore
authors.affiliation: School of Biosciences, University of Nottingham, Sutton Bonington, LE12 5RD, UK.
authors.forename: Michael
authors.initials: M
authors.lastname: Stout
authors.affiliation: Centre for Plant Integrative Biology, University of Nottingham, Sutton Bonington, LE12 5RD, UK.
authors.forename: Darren M
authors.initials: DM
authors.lastname: Wells
authors.affiliation: Centre for Plant Integrative Biology, University of Nottingham, Sutton Bonington, LE12 5RD, UK.
authors.forename: Michael H
authors.initials: MH
authors.lastname: Wilson
authors.affiliation: Centre for Plant Integrative Biology, University of Nottingham, Sutton Bonington, LE12 5RD, UK.
authors.forename: Malcolm J
authors.initials: MJ
authors.lastname: Bennett
authors.affiliation: School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
authors.forename: Oliver E
authors.identifier: http://orcid.org/0000-0003-0172-6578
authors.initials: OE
authors.lastname: Jensen
mesh_terms: D017360:Arabidopsis / Q000166:cytology / Q000254:growth & development / Q000502:physiology*; D002473:Cell Wall / Q000378:metabolism; D018522:Gravitropism; D055595:Mechanical Phenomena; D046529:Microscopy, Electron, Transmission; D008962:Models, Theoretical; D009928:Organ Specificity; D018517:Plant Roots / Q000166:cytology / Q000254:growth & development / Q000502:physiology*
keywords: Arabidopsis thaliana; elongation; extensibility; gravitropism; mechanical modelling; multiscale