title: Solutions for a local equation of anisotropic plant cell growth: an analytical study of expansin activity.
abstract: This paper presents a generalization of the Lockhart equation for plant cell/organ expansion in the anisotropic case. The intent is to take into account the temporal and spatial variation in the cell wall mechanical properties by considering the wall 'extensibility' (Φ), a time- and space-dependent parameter. A dynamic linear differential equation of a second-order tensor is introduced by describing the anisotropic growth process with some key biochemical aspects included. The distortion and expansion of plant cell walls initiated by expansins, a class of proteins known to enhance cell wall 'extensibility', is also described. In this approach, expansin proteins are treated as active agents participating in isotropic/anisotropic growth. Two-parameter models and an equation for describing α- and β-expansin proteins are proposed by delineating the extension of isolated wall samples, allowing turgor-driven polymer creep, where expansins weaken the non-covalent binding between wall polysaccharides. We observe that the calculated halftime (t(1/2) = εΦ(0) log 2) of stress relaxation due to expansin action can be described in mechanical terms.
authors.affiliation: Laboratory of Plant Physiology, Faculty of Biology and Environmental Protection, University of Silesia, Jagiellońska 28, 40032 Katowice, Poland. mariusz.pietruszka@us.edu.pl
authors.forename: Mariusz
authors.initials: M
authors.lastname: Pietruszka
mesh_terms: D016880:Anisotropy; D002473:Cell Wall / Q000502:physiology; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D063245:Plant Development; D010940:Plant Proteins / Q000502:physiology*
chemical_list: D010940:Plant Proteins; C095825:expansin protein, plant