  Worm-like filaments that are propelled homogeneously along their tangent
vector are studied by Brownian dynamics simulations. Systems in two dimensions
are investigated, corresponding to filaments adsorbed to interfaces or
surfaces. A large parameter space covering weak and strong propulsion, as well
as flexible and stiff filaments is explored. For strongly propelled and
flexible filaments, the free-swimming filaments spontaneously form stable
spirals. The propulsion force has a strong impact on dynamic properties, such
as the rotational and translational mean square displacement and the rate of
conformational sampling. In particular, when the active self-propulsion
dominates thermal diffusion, but is too weak for spiral formation, the
rotational diffusion coefficient has an activity-induced contribution given by
$v_c/\xi_P$, where $v_c$ is the contour velocity and $\xi_P$ the persistence
length. In contrast, structural properties are hardly affected by the activity
of the system, as long as no spirals form. The model mimics common features of
biological systems, such as microtubules and actin filaments on motility assays
or slender bacteria, and artificially designed microswimmers.
