2019/04/08 by Sven Bachmann, Bachmann, Sven, Richard Froese +3
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · #Biological Physics (physics.bio-ph) #FOS: Biological sciences #FOS: Physical sciences #Microtubule and mitosis dynamics #Plant Molecular Biology Research #Plant Reproductive Biology #Subcellular Processes (q-bio.SC)
paper · pdf · doi:10.48550/arxiv.1904.04328
openalex publication_date 2019/04/08 · openalex created_date 2022/07/24 · openalex updated_date 2026/07/28
In growing plant cells, parallel ordering of microtubules (MTs) along the\ninner surface of the cell membrane influences the direction of cell expansion\nand thereby plant morphology. For correct expansion of organs that primarily\ngrow by elongating, such as roots and stems, MTs must bend in the\nhigh-curvature direction along the cylindrically shaped cell membrane in order\nto form the required circumferential arrays. Computational studies, which have\nrecapitulated the self-organization of these arrays, ignored MT mechanics and\nassumed MTs follow geodesics of the cell surface. Here, we show, through\nanalysis of a derived Euler-Lagrange equation, that an elastic MT constrained\nto a cylindrical surface will deflect away from geodesics and toward low\ncurvature directions to minimize bending energy. This occurs when the curvature\nof the cell surface is relatively high for a given anchor density. In the limit\nof infinite anchor density, MTs always follow geodesics. We compare our\nanalytical predictions to measured curvatures and anchor densities and find\nthat the regime in which cells are forming these cortical arrays straddles the\nregion of parameter space in which arrays must form under the antagonistic\ninfluence of this mechanically induced deflection. Although this introduces a\npotential obstacle to forming circumferentially orientated arrays that needs to\nbe accounted for in the models, it also raises the question of whether plants\nuse this mechanical phenomenon to regulate array orientation. The model also\nconstitutes an elegant generalization of the classical Euler-bucking\ninstability along with an intrinsic unfolding of the associated pitchfork\nbifurcation.\n