  We describe the large-scale collective behavior of solutions of polar
biofilaments and both stationary and mobile crosslinkers. Both mobile and
stationary crosslinkers induce filament alignment promoting either polar or
nematic order. In addition, mobile crosslinkers, such as clusters of motor
proteins, exchange forces and torques among the filaments and render the
homogeneous states unstable via filament bundling. We start from a Smoluchowski
equation for rigid filaments in solutions, where pairwise crosslink-mediated
interactions among the filaments yield translational and rotational currents.
The large-scale properties of the system are described in terms of continuum
equations for filament and motor densities, polarization and alignment tensor
obtained by coarse-graining the Smoluchovski equation. The possible homogeneous
and inhomogeneous states of the systems are obtained as stable solutions of the
dynamical equations and are characterized in terms of experimentally accessible
parameters. We make contact with work by other authors and show that our model
allows for an estimate of the various parameters in the hydrodynamic equations
in terms of physical properties of the crosslinkers.
