On complex, curved trajectories in microtubule gliding

• We model the dynamics of microtubules in gliding assays.
• We explain the circular and wavy trajectories observed experimentally.
• We show that they are due to the helical nature of microtubules.
• Circular and wavy trajectories alternate as a function of filament length.

We study the dynamics of microtubules in gliding assays. These biofilaments are typically considered as purely semiflexible, hence their trajectories under the action of motors covering the substrate have been regarded so far as straight, modulo fluctuations. However, this is not always the case experimentally, where microtubules are known to move on large scale circles or spirals, or even display quite regular wavy trajectories and more complex dynamics. Incorporating recent experimental evidence for a (small) preferred curvature as well as the microtubules’ well established lattice twist into a dynamic model for microtubule gliding, we could reproduce both types of trajectories. Interestingly, as a function of the microtubules’ length we found length intervals of stable rings alternating with regions where wavy and more complex dynamics prevails. Finally, both types of dynamics (rings and waves) can be rationalized by considering simple limits of the full model.