Viscous damping of vibrations in microtubules

Pokorný et al. have recently suggested that metabolic processes drivemicrotubules in a cell to vibrate at Megahertz frequencies, but the theorydoes not explicitly consider dissipative effects which will tend to damp outthe vibrations. To examine the effects of viscous damping on the structure,we determine viscous forces and rate of energy loss in a cylinderundergoing longitudinal oscillations in water. A nondimensional expressionis obtained for the viscous drag on the cylinder. When applied to amicrotubule, the results indicate that viscous damping is several orders ofmagnitude too large to allow resonant vibrations.