  We formulate and analyze a theoretical model for the regulation of
microtubule (MT) polymerization dynamics by the signaling proteins Rac1 and
stathmin. In cells, the MT growth rate is inhibited by cytosolic stathmin,
which, in turn, is inactivated by Rac1. Growing MTs activate Rac1 at the cell
edge, which closes a positive feedback loop. We investigate both tubulin
sequestering and catastrophe promotion as mechanisms for MT growth inhibition
by stathmin. For a homogeneous stathmin concentration in the absence of Rac1,
we find a switch-like regulation of the MT mean length by stathmin. For
constitutively active Rac1 at the cell edge, stathmin is deactivated locally,
which establishes a spatial gradient of active stathmin. In this gradient, we
find a stationary bimodal MT length distributions for both mechanisms of MT
growth inhibition by stathmin. One subpopulation of the bimodal length
distribution can be identified with fast growing and long pioneering MTs in the
region near the cell edge, which have been observed experimentally. The
feedback loop is closed through Rac1 activation by MTs. For tubulin
sequestering by stathmin, this establishes a bistable switch with two stable
states: one stable state corresponds to upregulated MT mean length and bimodal
MT length distributions, i.e., pioneering MTs; the other stable state
corresponds to an interrupted feedback with short MTs. Stochastic effects as
well as external perturbations can trigger switching events. For catastrophe
promoting stathmin we do not find bistability.
