Modified Couple Stress Theory for Vibration of Embedded Bioliquid-Filled Microtubules under Walking a Motor Protein Including Surface Effects

Microtubules (MTs) are fibrous and tube-like cell substructures exist in cytoplasm of cells which play a vital role in many cellular processes. Surface effects on the vibration of bioliquid MTs surrounded by cytoplasm is investigated in this study. The emphasis is placed on the effect of the motor protein motion on the MTs. The MT is modeled as an orthotropic beam and the surrounded cytoplasm is assumed as an elastic media which is simulated by Pasternak foundation. In order to consider the small scale effects, the modified couple stress theory (MCST) is taken into account. An analytical method is employed to solve the motion equations obtained by energy method and Hamilton’s principle. The influence of surface layers, bioliquid, surrounding elastic medium, motor proteins motion, and small scale parameter are shown graphically. Results demonstrate that the speed of motor proteins is an effective parameter on the vibration characteristics of MTs. It is interesting that increasing the motor proteins speed does not change the maximum and minimum values of MTs dynamic deflection. The presented results might be useful in biomedical and biomechanical principles and applications.

Keywords:

Dynamic deflection , Motor protein movement , Bioliquid-filled microtubules , Cytoplasm , Modified couple stress theory