  The effect of interactions on dynamics of coupled motor proteins is
investigated theoretically. A simple stochastic discrete model, that allows to
calculate explicitly the dynamic properties of the system, is developed. It is
shown that there are two dynamic regimes, depending on the interaction between
the particles. For strong interactions the motor proteins move as one tight
cluster, while for weak interactions there is no correlation in the motion of
the proteins, and the particle separation increases steadily with time. The
boundary between two dynamic phases is specified by a critical interaction that
has a non-zero value only for the coupling of the asymmetric motor proteins,
and it depends on the temperature and the transitions rates. At the critical
interaction there is a change in a slope for the mean velocities and a
discontinuity in the dispersions of the motor proteins as a function of the
interaction energy.
