  We model analytically the dynamics of a cytoskeletal filament in a motility
assay. The filament is described as rigid rod free to slide in two dimensions.
The motor proteins consist of polymeric tails tethered to the plane and modeled
as linear springs and motor heads that bind to the filament. As in related
models of rigid and soft two-state motors, the binding/unbinding dynamics of
the motor heads and the dependence of the transition rates on the load exerted
by the motor tails play a crucial role in controlling the filament's dynamics.
Our work shows that the filament effectively behaves as a self-propelled rod at
long times, but with non-Markovian noise sources arising from the coupling to
the motor binding/unbinding dynamics. The effective propulsion force of the
filament and the active renormalization of the various friction and diffusion
constants are calculated in terms of microscopic motor and filament parameters.
These quantities could be probed by optical force microscopy.
