We studied the fluctuation in the translational sliding movement of microtubules driven by kinesin in a motility assay in vitro. By calculating the mean-square displacement deviation from the average as a function of time, we obtained motional diffusion coefficients for microtubules and analyzed the dependence of the coefficients on microtubule length. Our analyses suggest that 1) the motional diffusion coefficient consists of the sum of two terms, one that is proportional to the inverse of the microtubule length (as the longitudinal diffusion coefficient of a filament in Brownian movement is) and another that is independent of the length, and 2) the length-dependent term decreases with increasing kinesin concentration. This latter term almost vanishes within the length range we studied at high kinesin concentrations. From the length-dependence relationship, we evaluated the friction coefficient for sliding microtubules. This value is much larger than the solvent friction and thus consistent with protein friction. The length independence of the motional diffusion coefficient observed at sufficiently high kinesin concentrations indicates the presence of correlation in the sliding movement fluctuation. This places significant constraint on the possible mechanisms of the sliding movement generation by kinesin motors in vitro.
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