Kinesin walking effect on the size dependent vibration of bioliquid-filled microtubules

چکیده مقاله

MTs are objects made up of 12 to 17 protofilaments under in vitro conditions, and typically of 13 protofilaments in vivo. MTs almost always function in concert with the molecular motors that move on them. These motor proteins attach to different consignment, including organelles and vesicles, and pull them along the surface of the microtubule. MTs have vital roles in many cellular processes, as an example of forming the mitotic spindle, guiding and facilitating intracellular motions of organelles, and support kinesins to convert chemical energy into mechanical work. Motivated by these considerations, in this paper, size dependent vibration analysis of an embedded bioliquid-filled microtubule (MT) under a walking kinesin is investigated. The MT is assumed as an Euler-Bernoulli beam (EBB) model. The interactions between the MT and its surrounding elastic medium are simulated by Pasternak foundation model. The modified couple stress theory (MCST) is applied to consider small scale effects. The governing motion equations are derived using energy method and Hamilton’s principle. Finally the frequency of the bioliquid-filled MT is obtained analytically. The effects of surrounding elastic medium and small scale parameter on the normalized deflection of the MT are presented graphically. Results indicate that increasing small scale parameter decreases the deflection of the bioliquid-filled MT for both first and second modes. Also, increasing Winkler and Pasternak constants makes the system stiffer, therefore, the normalized deflection decreases with increasing elastic medium constants. Results of the present work is hoped to be of use in biomedical and biomechanical applications such as biosensors.