Ultrasensitivity of microtubule severing due to damage repair

Microtubule-based cytoskeletal structures aid in cell motility, cell polarization and intracellular transport. These functions require a coordinated effort of regulatory proteins which interact with microtubule cytoskeleton distinctively. In-vitro experiments have shown that free tubulin can repair nanoscale damages of microtubules created by severing proteins. Based on this observation, we theoretically analyze microtubule severing as a competition between the processes of damage spreading and tubulin-induced repair. We demonstrate that this model is in quantitative agreement with in-vitro experiments and predict the existence of a critical tubulin concentration above which severing becomes rare, fast, and sensitive to concentration of free tubulin. We show that this sensitivity leads to a dramatic increase in the dynamic range of steady-state microtubule lengths when the free tubulin concentration is varied, and microtubule lengths are controlled by severing. Our work demonstrates how synergy between tubulin and microtubule-associated proteins can bring about specific dynamical properties of microtubules.