  We analyse the dynamics of overlapping antiparallel treadmilling microtubules
in the presence of crosslinking processive motor proteins that counterbalance
an external force. We show that coupling the force-dependent velocity of motors
and the kinetics of motor exchange with a bath in the presence of treadmilling
leads generically to oscillatory behavior. In addition we show that coupling
the polymerization kinetics to the external force through the kinetics of the
crosslinking motors can stabilize the oscillatory instability into
finite-amplitude nonlinear oscillations and may lead to other scenarios,
including bistability.
