  We consider the dynamics of a bio-filament under the collective drive of
motor proteins. They are attached irreversibly to a substrate and undergo
stochastic attachment-detachment with the filament to produce a directed force
on it. We establish the dependence of the mean directed force and force
correlations on the parameters describing the individual motor proteins using
analytical theory and direct numerical simulations. The effective Langevin
description for the filament motion gives mean-squared displacement, asymptotic
diffusion constant, and mobility leading to an effective temperature. Finally,
we show how competition between motor protein extensions generates a self-load,
describable in terms of the effective temperature, affecting the filament
motion.
