Microtubule length distributions in the presence of protein-induced severing

TL;DR

This paper models microtubule length distributions considering protein-induced severing, revealing that severing does not alter microtubule quantity and providing analytical and numerical solutions for length distributions.

Contribution

Introduces a novel model for microtubule dynamics with severing, deriving analytical and numerical solutions for steady state length distributions.

Findings

Severing does not affect the number of microtubules.

Analytical expression derived for no rescue case.

Numerical solutions obtained for general case.

Abstract

Microtubules are highly regulated dynamic elements of the cytoskeleton of eukaryotic cells. One of the regulation mechanisms observed in living cells is the severing by the proteins katanin and spastin. We introduce a model for the dynamics of microtubules in the presence of randomly occurring severing events. Under the biologically motivated assumption that the newly created plus end undergoes a catastrophe, we investigate the steady state length distribution. We show that the presence of severing does not affect the number of microtubules, regardless of the distribution of severing events. In the special case in which the microtubules cannot recover from the depolymerizing state (no rescue events) we derive an analytical expression for the length distribution. In the general case we transform the problem into a single ODE that is solved numerically.