  Motivated by experiments on single-headed kinesin KIF1A, we develop a model
of intra-cellular transport by interacting molecular motors. It captures
explicitly not only the effects of ATP hydrolysis, but also the ratchet
mechanism which drives individual motors. Our model accounts for the
experimentally observed single molecule properties in the low density limit and
also predicts a phase diagram that shows the influence of hydrolysis and
Langmuir kinetics on the collective spatio-temporal organization of the motors.
Finally, we provide experimental evidence for the existence of domain walls in
our {\it in-vitro} experiment with fluorescently labeled KIF1A.
