Effect of viscoelastic medium on wave propagation along protein microtubules

An Orthotropic Kelvin-like model is developed here to study wave dispersion relation along microtubules when they are embedded in viscoelastic material. Owing anisotropicity of elastic shell like microtubules, an orthotropic elastic shell model is derived while the surrounding environment of microtubules is modeled as Kelvin like material. Symmetrical and asymmetrical waves are studied in embedded microtubules. We compared the wave velocities for embedded and free microtubules as well as the comparison of wave velocities for isotropic and orthotropic microtubules are also given. Longitudinal, Torsional and Radial wave velocities are obtained, noticing that torsional and radial wave velocities are lower in embedded microtubules as compared to longitudinal wave velocities in embedded microtubules. The radial wave frequency is considerably low because in cylindrical microtubules, pressure is exerted from the surroundings. The decrease in wave velocities is due to strong mechanical coupling of microtubules with surrounding medium and this decrement is more obvious when the wave length is long.