Daneshmand Farhang, Amabili Marco
School of Mechanical Engineering, Shiraz University, Shiraz, 71348-51154 Iran ; Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street W., Montreal, Québec Canada H3A 2K6.
J Biol Phys. 2012 Jun;38(3):429-48. doi: 10.1007/s10867-012-9263-y. Epub 2012 Feb 18.
Revealing vibration characteristics of sub-cellular structural components such as membranes and microtubules has a principal role in obtaining a deeper understanding of their biological functions. Nevertheless, limitations and challenges in biological experiments at this scale necessitates the use of mathematical and computational models as an alternative solution. As one of the three major cytoskeletal filaments, microtubules are highly anisotropic structures built from tubulin heterodimers. They are hollow cylindrical shells with a ∼ 25 nm outer diameter and are tens of microns long. In this study, a mechanical model including the effects of the viscous cytosol and surrounding filaments is developed for predicting the coupled oscillations of a single microtubule immersed in cytoplasm. The first-order shear deformation shell theory for orthotropic materials is used to model the microtubule, whereas the motion of the cytosol is analyzed by considering the Stokes flow. The viscous cytosol and the microtubule are coupled through the continuity condition across the microtubule-cytosol interface. The stress and velocity fields in the cytosol induced by vibrating microtubule are analytically determined. Finally, the influences of the dynamic viscosity of the cytosol, filament network elasticity, microtubule shear modulus, and circumferential wave-number on longitudinal, radial, and torsional modes of microtubule vibration are elucidated.
揭示诸如细胞膜和微管等亚细胞结构成分的振动特性对于更深入理解其生物学功能具有重要作用。然而，在此尺度下生物实验存在的局限性和挑战使得有必要使用数学和计算模型作为替代解决方案。作为三种主要的细胞骨架细丝之一，微管是由微管蛋白异二聚体构成的高度各向异性结构。它们是外径约25纳米、长度达数十微米的中空圆柱形外壳。在本研究中，开发了一个包含粘性细胞质溶胶和周围细丝影响的力学模型，用于预测浸没在细胞质中的单个微管的耦合振荡。采用正交各向异性材料的一阶剪切变形壳理论对微管进行建模，而通过考虑斯托克斯流来分析细胞质溶胶的运动。粘性细胞质溶胶和微管通过微管 - 细胞质溶胶界面处的连续性条件耦合。分析确定了振动微管在细胞质溶胶中引起的应力和速度场。最后，阐明了细胞质溶胶的动态粘度、细丝网络弹性、微管剪切模量和周向波数对微管振动的纵向、径向和扭转模式的影响。
