  Conventional kinesin walks by a hand-over-hand mechanism on the microtubule
(MT) by taking $\sim$ 8$nm$ discrete steps, and consumes one ATP molecule per
step. The time needed to complete a single step is on the order of twenty
microseconds. We show, using simulations of a coarse-grained model of the
complex containing the two motor heads, the MT, and the coiled coil that in
order to obtain quantitative agreement with experiments for the stepping
kinetics hydrodynamic interactions (HI) have to be included. In simulations
without hydrodynamic interactions spanning nearly twenty $\mu$s not a single
step was completed in hundred trajectories. In sharp contrast, nearly 14\% of
the steps reached the target binding site within 6$\mu$s when HI were included.
Somewhat surprisingly, there are qualitative differences in the diffusion
pathways in simulations with and without HI. The extent of movement of the
trailing head of kinesin on the MT during the diffusion stage of stepping is
considerably greater in simulations with HI than in those without HI. Our
results suggest that inclusion of HI is crucial in the accurate description of
motility of other motors as well.
