  We derive a model describing spatio-temporal organization of an array of
microtubules interacting via molecular motors. Starting from a stochastic model
of inelastic polar rods with a generic anisotropic interaction kernel we obtain
a set of equations for the local rods concentration and orientation. At large
enough mean density of rods and concentration of motors, the model describes an
orientational instability. We demonstrate that the orientational instability
leads to the formation of vortices and (for large density and/or kernel
anisotropy) asters seen in recent experiments. We derive the specific form of
the interaction kernel from the detailed analysis of microscopic interaction of
two filaments mediated by a moving molecular motor, and extend our results to
include variable motor density and motor attachment to the substrate.
