Fluctuations in sliding motion generated by independent and random actions of protein motors.

We consider theoretical fluctuations in the in vitro sliding movement of individual cytoskeletal filaments generated by an ensemble of protein motors whose actions are assumed to be statistically independent and random. We show that the mean square deviation of the sliding distances of a filament for a given period of time around their average is proportional to the inverse of the filament length. This result provides a basis for an experimental test of the general assumption on the independent and random actions of protein motors.