  Regulating physical size is an essential problem that biological organisms
must solve from the subcellular to the organismal scales, but it is not well
understood what physical principles and mechanisms organisms use to sense and
regulate their size. Any biophysical size-regulation scheme operates in a noisy
environment and must be robust to other cellular dynamics and fluctuations.
This work develops theory of filament length regulation inspired by recent
experiments on kinesin-8 motor proteins, which move with directional bias on
microtubule filaments and alter microtubule dynamics. Purified kinesin-8 motors
can depolymerize chemically-stabilized microtubules. In the length-dependent
depolymerization model, the rate of depolymerization tends to increase with
filament length, because long filaments accumulate more motors at their tips
and therefore shorten more quickly. When balanced with a constant filament
growth rate, this mechanism can lead to a fixed polymer length. However, the
mechanism by which kinesin-8 motors affect the length of dynamic microtubules
in cells is less clear. We study the more biologically realistic problem of
microtubule dynamic instability modulated by a motor-dependent increase in the
filament catastrophe frequency. This leads to a significant decrease in the
mean filament length and a narrowing of the filament length distribution. The
results improve our understanding of the biophysics of length regulation in
cells.
