  We present a generic coarse-grained model to describe molecular motors acting
on polymer substrates, mimicking, for example, RNA polymerase on DNA or kinesin
on microtubules. The polymer is modeled as a connected chain of beads; motors
are represented as freely diffusing beads which, upon encountering the
substrate, bind to it through a short-ranged attractive potential. When bound,
motors and polymer beads experience an equal and opposite active force,
directed tangential to the polymer; this leads to motion of the motors along
the polymer contour. The inclusion of explicit motors differentiates our model
from other recent active polymer models. We study, by means of Langevin
dynamics simulations, the effect of the motor activity on both the
conformational and dynamical properties of the substrate. We find that activity
leads, in addition to the expected enhancement of polymer diffusion, to an
effective reduction of its persistence length. We discover that this effective
"softening" is a consequence of the emergence of double-folded branches, or
hairpins, and that it can be tuned by changing the number of motors or the
force they generate. Finally, we investigate the effect of the motors on the
probability of knot formation. Counter-intuitively our simulations reveal that,
even though at equilibrium a more flexible substrate would show an increased
knotting probability, motor activity leads to a marked decrease in the
occurrence of knotted conformations with respect to equilibrium.
