  Length-regulation of microtubules (MTs) is essential for many cellular
processes. Molecular motors like kinesin 8, which move along MTs and also act
as depolymerases, are known as key players in MT dynamics. However, the
regulatory mechanisms of length control remain elusive. Here, we investigate a
stochastic model accounting for the interplay between polymerization kinetics
and motor-induced depolymerization. We determine the dependence of MT length
and variance on rate constants and motor concentration. Moreover, our analyses
reveal how collective phenomena lead to a well-defined MT length.
