The self-organization of plant microtubules in three dimensions enables stable cortical localization and sensitivity to external cues

Many cell functions rely on the ability of microtubules to self-organize as complex networks. In plants, cortical microtubules are essential to determine cell shape as they guide the deposition of cellulose microfibrils, and thus control mechanical anisotropy in the cell wall. Here we analyze how, in turn, cell shape may influence microtubule behavior. Using a computational model of microtubules enclosed in a three-dimensional space, We show that the microtubule network has spontaneous configurations that could explain many experimental observations without resorting to specific regulation. In particular, we find that the preferred localization of microtubules at the cortex emerges from directional persistence of the microtubules, combined with their growth mode. We identified microtubule parameters that seem relatively insensitive to cell shape, such as length or number. In contrast, microtubule array anisotropy depends strongly on local curvature of the cell surface and global orientation follows robustly the longest axis of the cell. Lastly, we found that the network is capable of reorienting toward weak external directional cues. Altogether our simulations show that the microtubule network is a good transducer of weak external polarity, while at the same time, it easily reaches stable global configurations.