  Inspired by recent experiments on chromosomal dynamics, we introduce an
exactly solvable model for the interaction between a flexible polymer and a set
of motor-like enzymes. The enzymes can bind and unbind to specific sites of the
polymer and when bound produce a dipolar force on two neighboring monomers. We
study the resulting non-equilibrium dynamics of the polymer and find that the
motion of the monomers has several properties that were observed experimentally
for chromosomal loci: a subdiffusive mean squared displacement and the
appearance of regions of correlated motion. We also determine the velocity
autocorrelation of the monomers and find that the underlying stochastic process
is not fractional Brownian motion. Finally, we show that the active forces
swell the polymer by an amount that becomes constant for large polymers.
