Cell geometry, microtubule anchoring and anisotropic dynamic instability: challenges and solutions to transverse cortical array organization

The self-organization of cortical microtubules within plant cells is an emergent phenomenon with important consequences for the synthesis of the cell wall, cell shape, and subsequently the structure of plants. Mathematical modelling and experiments have elucidated the underlying processes involved. There has been recent interest in the influence of geometric cues on array orientation, be it direct (cell shape) or indirect (tension in the membrane). However, the mechanical influence of membrane curvature on these elastic filaments has largely been ignored. A previous model was proposed to describe how the anchoring process may control the shape of individual microtubules seeking to minimize bending on a cylindrical cell. We implement this process into a model of interacting microtubules and find the cell curvature influence should be significant: the array favours orientations parallel to the direction of elongation rather than the expected transverse direction. Even without elasticity, the geometry of large cells hinders robust microtubule organization. These results suggest the necessity of additional processes to overcome these factors. We propose a simple model of orientation-dependent catastrophe in the context of cellulose microfibrils impeding microtubule polymerization and find a moderate impedance to be sufficient to generate transverse arrays despite the geometric influences.