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

The self-organization of cortical microtubule 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 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 deflection of individual microtubules seeking to minimize bending on a cylindrical cell. We incorporate this process into a model of interacting microtubules and find the cell curvature influence to 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 an orientation-dependent catastrophe rate, hypothetically caused by cellulose microfibrils impeding microtubule polymerization. We find a combination of anchoring and impedance to be sufficient to generate transverse arrays despite the geometric influences. Significance Statement The organization of microtubule (MT) polymers into parallel arrays along the two-dimensional cortex of plant cells is crucial for directional cell growth and plant development. Despite decades of experimentation and more recent computational modelling, understanding the mechanisms that orient cortical MTs remains incomplete. With computational modelling, we have re-examined an assumption common to many models: that MTs grow along straight (geodesic) paths rather than minimizing bending. We model MT bending, and find a significant disruption of transverse MT ordering, especially in larger cells. We find that angle-dependent MT behaviour can counteract the effect of bending in certain contexts.