一种用于模拟柔性纤维悬浮体的快速平台及其在细胞力学中的应用
A fast platform for simulating flexible fiber suspensions applied to cell mechanics
AI总结：
本文提出一种快速平台，用于模拟浸没在斯托克斯流体中的纤维结构在受限空间或自由空间中的大尺度模拟，通过非局部细长体理论和边界积分方法，研究细胞内纤维组装的动力学。
摘要：
我们提出了一种新的平台，用于大规模模拟浸没在斯托克斯流体中的纤维结构，并在受限空间或自由空间中演变。主要动机是研究生物细胞内纤维组装的动力学。为此，我们还整合了决定这些组装体动力学的关键生物物理元素，包括纤维的聚合和脱聚动力学、其与分子马达和其他物体的相互作用、其柔性和流体动力学耦合。这项工作，据我们所知，是首次将多体流体动力学相互作用（HIs）及其产生的流体流动纳入细胞纤维组装中的技术。我们使用非局部细长体理论计算纤维的流体-结构相互作用，并使用第二种类型的边界积分公式计算其他刚体和限制边界。采用不依赖核的快速多重方法实现高效评估HIs。纤维的变形由非线性欧拉-伯努利梁理论描述，其聚合通过在适当的非拉格朗日框架中重新参数化动态方程来建模。我们使用伪谱表示纤维位置，并在时间步进中使用隐式HIs来解决大纤维变形，并允许时间步长不受时间刚度或纤维-纤维相互作用的限制。整个计算方案被并行化，使能够模拟成千上万的纤维组装。我们使用该方法研究了细胞分裂力学中的两个重要问题：（i）限制对微管星的流体动力学移动的影响；（ii）复杂细胞几何中分裂极体定位的动力学。
英文摘要：
We present a novel platform for the large-scale simulation of fibrous structures immersed in a Stokesian fluid and evolving under confinement or in free-space. One of the main motivations for this work is to study the dynamics of fiber assemblies within biological cells. For this, we also incorporate the key biophysical elements that determine the dynamics of these assemblies, which include the polymerization and depolymerization kinetics of fibers, their interactions with molecular motors and other objects, their flexibility, and hydrodynamic coupling. This work, to our knowledge, is the first technique to include many-body hydrodynamic interactions (HIs), and the resulting fluid flows, in cellular fiber assemblies. We use the non-local slender body theory to compute the fluid-structure interactions of the fibers and a second-kind boundary integral formulation for other rigid bodies and the confining boundary. A kernel-independent implementation of the fast multiple method is utilized for efficient evaluation of HIs. The deformation of the fibers is described by the nonlinear Euler--Bernoulli beam theory and their polymerization is modeled by the reparametrization of the dynamic equations in the appropriate non-Lagrangian frame. We use a pseudo-spectral representation of fiber positions and implicit HIs in the time-stepping to resolve large fiber deformations, and to allow time-steps not constrained by temporal stiffness or fiber-fiber interactions. The entire computational scheme is parallelized, which enables simulating assemblies of thousands of fibers. We use our method to investigate two important questions in the mechanics of cell division: (i) the effect of confinement on the hydrodynamic mobility of microtubule asters; and (ii) the dynamics of the positioning of mitotic spindle in complex cell geometries.
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