  We use single-particle tracking to study the elastic properties of single
microtubules grafted to a substrate. Thermal fluctuations of the free
microtubule's end are recorded, in order to measure position distribution
functions from which we calculate the persistence length of microtubules with
contour lengths between 2.6 and 48 micrometers. We find the persistence length
to vary by more than a factor of 20 over the total range of contour lengths.
Our results support the hypothesis that shearing between protofilaments
contributes significantly to the mechanics of microtubules.
