  Motor proteins that specifically interact with the ends of cytoskeletal
filaments can induce filament depolymerization. A phenomenological description
of this process is presented. We show that under certain conditions motors
dynamically accumulate at the filament ends. We compare simulations of two
microscopic models to the phenomenological description. The depolymerization
rate can exhibit maxima and dynamic instabilities as a function of the bulk
motor density for processive depolymerization. We discuss our results in
relation to experimental studies of Kin-13 family motor proteins.
