Analysis of wave propagation in orthotropic microtubules embedded within elastic medium by Pasternak model

Deformation pattern in vibrating microtubule: Structural mechanics study based on an atomistic approach

The mechanical properties of microtubules are of great importance for understanding their biological function and for applications in artificial devices. Although microtubule mechanics has been extensively studied both theoretically and experimentally, the relation to its molecular structure is understood only partially. Here, we report on the structural analysis of microtubule vibration modes calculated by an atomistic approach. Molecular dynamics was applied to refine the atomic structure of a microtubule and a C_α elastic network model was analyzed for its normal modes. We mapped fluctuations and local deformations up to the level of individual aminoacid residues. The deformation is mode-shape dependent and principally different in α-tubulins and β-tubulins. Parts of the tubulin dimer sequence responding specifically to longitudinal and radial stress are identified. We show that substantial strain within a microtubule is located both in the regions of contact between adjacent dimers and in the body of tubulins. Our results provide supportive evidence for the generally accepted assumption that the mechanics of microtubules, including its anisotropy, is determined by the bonds between tubulins.

Vibration of bioliquid-filled microtubules embedded in cytoplasm including surface effects using modified couple stress theory

This paper aims to investigate vibrational behavior of bioliquid-filled microtubules (MTs) embedded in cytoplasm considering surface effects. The interactions between the MT, considered as an orthotropic beam within the framework of Euler-Bernoulli beam (EBB) and Timoshenko beam (TB) models, and its surrounding elastic media are simulated by Pasternak foundation model. The modified couple stress theory (MCST) is applied so as to consider the small scale effects while motion equations are derived using energy method and Hamilto's principle for both EBB and TB models. Finally, an analytical method is employed to obtain the frequency of a bioliquid-filled MT, and therefore frequency-response curves are plotted to investigate the influences of small scale parameter, mass density of bioliquid, surface layer and surrounding elastic medium graphically. The results indicate that bioliquid and surface layers play a key role on the frequency of MTs and that the frequency of MTs is decreased with increasing of the mass density of the bioliquid. Vibration analysis of MTs is being considered as a vital problem since MTs look like the nervous system of the biological cells and transmit vibrational signals. It should be noted that the results of this work are hoped to be of use in advanced medical applications especially in the forthcoming use of MTs in transporters for bio-nanosensors.