  The cytoskeleton is regulated by a plethora of enzymes that influence the
stability and dynamics of cytoskeletal filaments. Molecular motors of the
kinesin-8 protein family depolymerise microtubules in a length-dependent
manner, and experimental and theoretical evidence suggest a role for kinesin-8
in the dynamic regulation of microtubules. However, so far the detailed
molecular mechanisms how these molecular motors interact with the growing
microtubule tip remain elusive. Here we investigate two interaction scenarios
for kinesin-8 and the microtubule tip. We give a comprehensive analysis of
regimes where length-regulation is possible and characterise how the stationary
length depends on the biochemical rates and the bulk concentrations of the
various proteins. For a neutral scenario, where microtubules grow irrespective
of whether the microtubule tip is occupied by a molecular motor, length
regulation is possible only for a narrow range of biochemical rates and limited
to small polymerisation rates. In contrast, for an inhibition scenario, where
the presence of a motor at the microtubule tip inhibits microtubule growth, the
regime of length regulation is extremely broad and includes high growth rates.
These results also apply to situations where polymerising enzymes, like
XMAP215, and kinesin-8 mutually exclude each other from the microtubule tip. We
also investigate the stochastic dynamics of the two scenarios. While for the
neutral scenario length is tightly controlled, length dynamics is intermittent
for the inhibition scenario and exhibits extended periods of microtubule growth
and shrinkage, reminiscent of microtubule dynamic instability. On a broader
perspective, the set of models established in this work quite generally
suggests that mutual exclusion of molecules at the ends of cytoskeletal
filaments is an important factor for filament dynamics and regulation.
