  Large scale motion of cytoplasm called cytoplasmic streaming occurs in some
large eukaryotic cells to stir the cell's constituents. In Drosophila oocytes,
microtubules have been observed to undergo undulating motion, curving to form
travelling waves during cytoplasmic streaming. Here we show that this wave-like
motion can be understood physically as due to the hydrodynamic drag of
streaming impellers attached to kinesin motors moving toward the plus-ends of
microtubules whose minus ends are anchored to the cell cortex. The tangential
forces applied to such microtubules by kinesin give rise to bending and leads
to chiral symmetry breaking causing the microtubules to propagate long
travelling waves. The waves are reminiscent of those seen in flagellar motion
but of a much longer time scale and by a different physical mechanism. We show
how kinesin movement can produce a bulk flow of cytoplasm surrounding a
microtubule with the range of flow greatly enhanced by the effect of
hydrodynamic coupling between impellers. That is, a relatively small number of
motors can move a large amount of fluid. The chaotic nature of the fluid motion
of cytoplasm caused by kinesin movement along constantly changing microtubule
trajectories is important as it greatly enhances the efficiency of mixing.
Existing data on in vitro microtubule gliding assays also show this chiral
instability in two dimensions and an analysis of this gives quantitative
estimates for the forces exerted by motors and the drag coefficient.
