  Inspired by recent experiments on the dynamics of particles and polymers in
artificial cytoskeletons and in cells, we introduce a modified Langevin
equation for a particle in an environment that is a viscoelastic medium and
that is brought out of equilibrium by the action of active fluctuations caused
by molecular motors. We show that within such a model, the motion of a free
particle crosses over from superdiffusive to subdiffusive as observed for
tracer particles in an {\it in vitro} cytoskeleton or in a cell. We investigate
the dynamics of a particle confined by a harmonic potential as a simple model
for the motion of the tethered head of kinesin-1. We find that the probability
that the head is close to its binding site on the microtubule can be enhanced
by a factor of two due to active forces. Finally, we study the dynamics of a
particle in a double well potential as a model for the dynamics of
DNA-hairpins. We show that the active forces effectively lower the potential
barrier between the two minima and study the impact of this phenomenon on the
zipping/unzipping rate.
