Elastic vibrations of microtubules in a fluid

We study theoretically vibrational properties of microtubules (MTs), which are long hollow cylindrical macromolecules with a diam. of the order of 25 nm and serve as a major component of cytoskeleton in eukariotic cells. Modeling MTs by thin elastic cylindrical shells, we derive the eigenfrequencies and eigenmodes of confined elastic vibrations in a shell-fluid system. Numerical calculations, based on recently obtained experimental data for Young's modulus of MT, show that MT-water system supports interface elastic waves with maximal frequencies in a gigahertz range. In a long-wavelength limit, there exist three axisymmetric acoustic waves with velocities of about 200 to 600 m/s, and an infinite set of helical waves with a parabolic dispersion law.