Vibration analysis of a single microtubule surrounded by cytoplasm

Microtubules are the central part of the cytoskeleton in eukaryotic cells. The microtubules immersed in the cytoplasm are in contact with water and other cytoplasmic molecules. In this study, a mechanics model of microtubule vibration, considering the coupled effect of the viscoelastic surrounding cytoplasm, is analytically investigated. The microtubule is modeled as a linear elastic cylindrical tube. The cytoplasm is characterized by viscous cytosol and elastic filaments network. The cytosol motion is modeled as the Stokes flow with no-slip condition at the microtubule–cytosol interface. The stress field in the cytosol induced by vibrating microtubule is determined, the effect of the surrounding filament network is considered and the coupled vibrations of the microtubule–cytoplasm system are investigated. The variations of damped-frequencies with the cytosol dynamic viscosity, microtubule bending stiffness, microtubule length and the elastic modulus of the surrounding filament network are also examined.