  Enzymatic molecules that actively support many cellular processes, including
transport, cell division and cell motility, are known as motor proteins or
molecular motors. Experimental studies indicate that they interact with each
other and they frequently work together in large groups. To understand the
mechanisms of collective behavior of motor proteins we study the effect of
interactions in the transport of molecular motors along linear filaments. It is
done by analyzing a recently introduced class of totally asymmetric exclusion
processes that takes into account the intermolecular interactions via
thermodynamically consistent approach. We develop a new theoretical method that
allows us to compute analytically all dynamic properties of the system. Our
analysis shows that correlations play important role in dynamics of interacting
molecular motors. Surprisingly, we find that the correlations for repulsive
interactions are weaker and more short-range than the correlations for the
attractive interactions. In addition, it is shown that symmetry of interactions
affect dynamic properties of molecular motors. The implications of these
findings for motor proteins transport are discussed. Our theoretical
predictions are tested by extensive Monte Carlo computer simulations.
