Ultrasensitivity of Microtubule severing rate on the concentration of free Tubulin

Cytoskeletal structures aid in cell polarization, motility, and intracellular transport. Their functions are predicated on the rapid turnover of cytoskeleton proteins, which is achieved by the coordinated effort of multiple regulatory proteins whose dynamics are not well understood. In-vitro experiments have shown that free tubulin can repair nanoscale damages of microtubules created by severing proteins. Based on this observation, we propose a model for microtubule severing as a competition between the processes of damage spreading and tubulin-induced repair. Using theory and simulations, we demonstrate that this model is in quantitative agreement with in vitro experiments. We predict the existence of a critical tubulin concentration above which severing becomes rare but fast, and hypersensitive to the concentration of free tubulin. Further we show that this hypersensitivity leads to a dramatic increase in the dynamic range of steady-state microtubule lengths, when lengths are controlled by severing. Our work demonstrates how synergy between tubulin and severing proteins can lead to novel dynamical properties of microtubules.