The Buckling Behavior And The Vibration-induced Electric Field Effect Of A Microtubule

Microtubules (MTs), actin filaments and intermediate filaments are principal components of cytoskeleton structure, in which MTs play essential roles in a multitude of cellular functions in all eukaryotes, such as maintain the shape of the cell, sustain the external force and provide mechanical strength to the cell. As the stiffest component of the cytoskeleton structure, MTs show sufficient resistance to bending in large scale as well as remarkable resiliency in small scales. Therefore, a through understanding of MT mechanical properties and the electromagnetic properties are important not only in elucidating the biological functions of MTs but also particularly useful on designing of biomechanical system in nanometer and micrometer scale. This thesis is focusing on investigating the mechanical behavior and electromagnetic properties of MTs, the concretions are listed below:Firstly, we used the nonlocal elastic model which was widely applicable to nano and micro scale and the worm-like chain model which was applied to the biological large molecular to establish the MT nonlocal anisotropic shell model for investigating the persistence length. The results showed that the small scale effects has large effects on the persistence length when the contour length is short and has nearly no effects when the contour length was large, the model was also used to verify that the persistence length was length-dependent.Secondly, based on the nonlocal anisotropic shell model, this paper gave the expressions of buckling growth rate, critical buckling and the free vibrations with the influence of the cytoplasm. The filaments network was modeled as an elastic foundation, and the cytosol streaming as the Stokes flow. The microtubules buckling growth rate which was proposed by Li was used to investigate dynamic buckling behavior and to explain the short wave buckling behavior. The numerical simulation showed that the small scale effects, the shear modulus, the viscosity of the cytosol, and the elastic modulus of the filaments network et al. had important impact on the critical buckling and buckling growth rate. Moreover, the influence of the small scale effect can not be ignored to investigate the free vibration mode of microtubule in cytoplasm.The longitudinal vibration of microtubule can generate electromagnetic field around it. The longitudinal angular frequency with the influence of the small scale parameters, longitudinal half-wave number and contour length directly affected the electric field spatial distribution. Consider the cytoplasm around the MT as an isotropic, unbounded and passive conductive medium, and the heterodimer as a dipole moment. The electric field of the sine-deformed MT with the coherent vibration mode and the random vibration mode were derived respectively. The results showed that the deformation of the MT and the frequency, the contour length and the vibration excitation had important influence on the electric distribution, including the magnitude and the orientation.