  The collective dynamics of $N$ weakly coupled processive molecular motors are
considered theoretically. We show, using a discrete lattice model, that the
velocity-force curves strongly depend on the effective dynamic interactions
between motors and differ significantly from a simple mean field prediction.
They become essentially independent of $N$ if it is large enough. For strongly
biased motors such as kinesin this occurs if $N\gtrsim 5$. The study of a
two-state model shows that the existence of internal states can induce
effective interactions.
