We have studied the dependence on microtubule length of sliding velocity and positional fluctuation from recorded trajectories of microtubules sliding over sea urchin sperm outer arm β dynein in a motility assay in vitro. The positional fluctuation was quantified by calculating the mean-square displacement deviation from the average, the calculation of which yields an effective diffusion coefficient. We have found that (1) the sliding velocity depends hyperbolically on the microtubule length, and (2) the effective diffusion coefficients do not depend on the length for sufficiently long microtubules. The length dependence of the sliding velocity indicates that the duty ratio, defined as the force producing period over the total cycle time of β dynein interaction with microtubule, is very small. The length independence of the effective diffusion coefficient indicates that there is a correlation in the sliding movement fluctuation of microtubules.
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