Collective dynamics of molecular motors pulling on fluid membranes

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.