Conflicting roles of cell geometry, microtubule deflection, and orientation-dependent dynamic instability in cortical array organization.

The self-organization of cortical microtubule (MT) arrays 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 modeling 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 deflection of individual MTs seeking to minimize bending on a cylindrical cell. We incorporate this process into a model of interacting MTs and find the cell curvature influence to be significant: the array favors orientations parallel to the direction of elongation rather than the expected transverse direction. Even without elasticity, the geometry of large cells hinders robust MT organization. These results suggest the necessity of additional processes to overcome these factors. We propose an orientation-dependent catastrophe rate, hypothetically caused by cellulose microfibrils impeding MT polymerization. We find a combination of anchoring and impedance to be sufficient to generate transverse arrays despite the geometric influences.