Feng Yan, Mitran Sorin
Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3250.
Cytoskeleton (Hoboken). 2018 Feb;75(2):45-60. doi: 10.1002/cm.21419. Epub 2017 Nov 30.
A beam element is constructed for microtubules based upon data reduction of the results from atomistic simulation of the carbon backbone chain of αβ-tubulin dimers. The database of mechanical responses to various types of loads from atomistic simulation is reduced to dominant modes. The dominant modes are subsequently used to construct the stiffness matrix of a beam element that captures the anisotropic behavior and deformation mode coupling that arises from a microtubule's spiral structure. In contrast to standard Euler-Bernoulli or Timoshenko beam elements, the link between forces and node displacements results not from hypothesized deformation behavior, but directly from the data obtained by molecular scale simulation. Differences between the resulting microtubule data-driven beam model (MTDDBM) and standard beam elements are presented, with a focus on coupling of bending, stretch, shear deformations. The MTDDBM is just as economical to use as a standard beam element, and allows accurate reconstruction of the mechanical behavior of structures within a cell as exemplified in a simple model of a component element of the mitotic spindle.
基于对αβ-微管蛋白二聚体碳主链原子模拟结果的数据简化，构建了一种用于微管的梁单元。将原子模拟中各种载荷的力学响应数据库简化为主要模式。随后，这些主要模式被用于构建梁单元的刚度矩阵，该矩阵捕捉了微管螺旋结构产生的各向异性行为和变形模式耦合。与标准的欧拉-伯努利梁单元或铁木辛柯梁单元不同，力与节点位移之间的联系并非源于假设的变形行为，而是直接来自分子尺度模拟获得的数据。给出了所得的微管数据驱动梁模型（MTDDBM）与标准梁单元之间的差异，重点关注弯曲、拉伸、剪切变形的耦合。MTDDBM的使用与标准梁单元一样经济，并能准确重建细胞内结构的力学行为，如在有丝分裂纺锤体组成元件的简单模型中所示。
