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J Cell Biol. 1993 Feb;120(4):923-34.

Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape.

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Department of Physiology and Biophysics, University of Washington, Seattle 98195.


Microtubules are long, proteinaceous filaments that perform structural functions in eukaryotic cells by defining cellular shape and serving as tracks for intracellular motor proteins. We report the first accurate measurements of the flexural rigidity of microtubules. By analyzing the thermally driven fluctuations in their shape, we estimated the mean flexural rigidity of taxol-stabilized microtubules to be 2.2 x 10(-23) Nm2 (with 6.4% uncertainty) for seven unlabeled microtubules and 2.1 x 10(-23) Nm2 (with 4.7% uncertainty) for eight rhodamine-labeled microtubules. These values are similar to earlier, less precise estimates of microtubule bending stiffness obtained by modeling flagellar motion. A similar analysis on seven rhodamine-phalloidin-labeled actin filaments gave a flexural rigidity of 7.3 x 10(-26) Nm2 (with 6% uncertainty), consistent with previously reported results. The flexural rigidity of these microtubules corresponds to a persistence length of 5,200 microns showing that a microtubule is rigid over cellular dimensions. By contrast, the persistence length of an actin filament is only approximately 17.7 microns, perhaps explaining why actin filaments within cells are usually cross-linked into bundles. The greater flexural rigidity of a microtubule compared to an actin filament mainly derives from the former's larger cross-section. If tubulin were homogeneous and isotropic, then the microtubule's Young's modulus would be approximately 1.2 GPa, similar to Plexiglas and rigid plastics. Microtubules are expected to be almost inextensible: the compliance of cells is due primarily to filament bending or sliding between filaments rather than the stretching of the filaments themselves.

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