Predicted effects of severing enzymes on the length distribution and total mass of microtubules

Microtubules are dynamic cytoskeletal polymers whose growth and shrinkage are highly regulated as eukaryotic cells change shape, move and divide. One family of microtubule regulators includes the ATP-hydrolyzing enzymes spastin, katanin and fidgetin, which sever microtubule polymers into shorter fragments. Paradoxically, severases can increase microtubule number and mass in cells. Recent work with purified spastin and katanin accounts for this phenotype by showing that, in addition to severing, these enzymes modulate microtubule dynamics by accelerating the conversion of microtubules to the growing state and thereby promoting their regrowth. This leads to the observed exponential increase in microtubule mass. Spastin also influences the steady-state distribution of microtubule lengths, changing it from an exponential, as predicted by models of microtubule dynamic instability, to a peaked distribution. This effect of severing and regrowth by spastin on the microtubule length distribution has not been explained theoretically. To solve this problem, we formulated and solved a master equation for the time evolution of microtubule lengths in the presence of severing and microtubule dynamic instability. We then obtained numerical solutions to the steady-state length distribution and showed that the rate of severing and the speed of microtubule growth are the dominant parameters determining the steady-state length distribution. Furthermore, we found that the amplification rate is predicted to increase with severing, which is a new result. Our results establish a theoretical basis for how severing and dynamics together can serve to nucleate new microtubules, constituting a versatile mechanism to regulate microtubule length and mass. Significance The numbers and lengths of microtubules are tightly regulated in cells. Severing enzymes fragment microtubules into shorter filaments and are important for cell division and tissue development. Previous work has shown that severing can lead to an increase in total microtubule number and mass, but the effect of severing on microtubule length is not understood quantitatively. Combining mathematical modeling and computational simulation, we solve the microtubule length distribution in the presence of severing enzymes and explore how severing activity and microtubule dynamics collectively control microtubule number and length. These results advance our understanding of the physical basis of severing as a regulatory mechanism shaping the cellular cytoskeletal network.