Finite Element Simulation Of Mechanical Properties Of Microtubules

The cell is a basic structure and function unit of the organism. The structure stiffness and geometry of a cell is determined by the cytoskeleton extentively. The main components of the cytoskeleton are microtubule, microfilament and middle fiber. These polymer are very important for intracellular protein material transporting,the movement of the organelles, chromosome movement during the process of mitosis and the formation of the cell wall.Microtubules are the highest intensity of cytoskeleton components, the axial stiffness was significantly higher than that of microfilament and intermediate fiber stiffness, but show the high flexibility when bending. To study the relationship between mechanical properties and structure of the microtubules can promote further to understanding the mechanism of the physiological processes of living organisms and promote the development of biomimetic materials science. Especially the sliding between adjacent protofilaments of microtubules has been observed in the experiment, the sliding has a great effect on the mechanical property of microtubules. So this article will discuss issues related to the following two aspects of research:The effect of sliding between adjacent protofilaments on the performance of the microtubules bending. Adopting the molecular structural mechanics model of the microtubules, the interactions between the adjacent protofilaments characterized with equivalent beam elements Beam2. The bending moment and transverse force are applied at the free end of the model respectively, by changing the three stiffness of Beam2, that is the three stiffness respectively change into（6 610 10--）times of the original value, to discuss the generative conditions of the sliding between adjacent protofilaments and under different boundary conditions to compute the bending deflection of microtubules and equivalent bending stiffness. Results show that the sliding is a main reason about the equivalent bending rigidity of microtubule change with the length. The study of relationship between microtubule structure and its mechanical behavior can provide useful guidance to the designing of the intelligent materials and research in the future. For example, the research results show that, bychanging the interaction force between protofilaments can control the bending performance.The effect of sliding between adjacent protofilaments on the performance of the microtubules vibrating. The frequencies of free vibrating of microtubules is calculated by the classical Euler beam model and compared with the frequencies based on the molecular structure mechanical model.Under two different boundary conditions（both ends fixed supported and cantilever）, the Euler beam model overestimated the transverse free vibrating frequency of microtubules（length-diameter ratio L / D 310）. With the increase of the mode of vibrating or decrease of the "wavelength- diameter" ratio, the error between Euler beam model and the molecular structure mechanical model becomes larger.This difference can be explained through the nonlocal theory. In the bending of microtubules, the sliding between adjacent protofilaments provides the physical source of the nonlocal parameterse₀a. Before this, the physical origin of the nonlocal parameterse₀a in nonlocal mechanics theory hasn’t been able to get a clear explanation. This finding indicates that the effect of nonlocal effects in the microtubule reduces the frequency of free vibrating of microtubules through the sliding between the adjacent protofilaments, the degree of the sliding can be characterized by the nonlocal parametere₀a.