Vibration of protein microtubules via scale-dependent continuum models

Increasing the level of knowledge on the mechanics of biological structures such as protein microtubules is important because of two main reasons. The first reason is that the biological properties of living organisms are highly affected by their mechanical properties such as their elasticity modulus and resonance natural frequencies. Secondly, the mechanical properties and characteristics can be used as a clue in order to analyze the performance and functionality of a living organism. In this paper, the pioneering research studies on the vibrational behavior of protein microtubules as an important part of the cytoplasm are reviewed. Two widely used theoretical approaches, namely the pure nonlocal and nonlocal strain gradient models, are proposed. The natural frequencies of microtubules are strongly influenced by the stress nonlocality and the half wave number along the axial direction.