Semiflexible slender filaments are ubiquitous in nature and cell biology, including in the cytoskeleton, where reorganization of actin filaments allows the cell to move and divide. Most methods for simulating semiflexible inextensible fibers/polymers are based on discrete (bead-link or blob-link) models, which become prohibitively expensive in the slender limit when hydrodynamics is accounted for. In this paper, we develop a novel coarse-grained approach for simulating fluctuating slender filaments with hydrodynamic interactions. Our approach is tailored to relatively stiff fibers whose persistence length is comparable to or larger than their length, and is based on three major contributions. First, we discretize the filament centerline using a coarse non-uniform Chebyshev grid, on which we formulate a discrete constrained Gibbs-Boltzmann equilibrium distribution and overdamped Langevin equation. Second, we define the hydrodynamic mobility at each point on the filament as an integral of the Rotne-Prager-Yamakawa kernel along the centerline, and apply a spectrally-accurate quadrature to accurately resolve the hydrodynamics. Third, we propose a novel midpoint temporal integrator which can correctly capture the Ito drift terms that arise in the overdamped Langevin equation. We verify that the equilibrium distribution for the Chebyshev grid is a good approximation of the blob-link one, and that our temporal integrator samples the equilibrium distribution for sufficiently small time steps. We also study the dynamics of relaxation of an initially straight filament, and find that as few as 12 Chebyshev nodes provides a good approximation to the dynamics while allowing a time step size two orders of magnitude larger than a resolved blob-link simulation. We conclude by studying how bending fluctuations aid the process of bundling in cross-linked networks of semiflexible fibers.

翻译：半柔性细丝在自然界和细胞生物学中无处不在，包括在细胞骨架中，其中肌动蛋白丝的重组使细胞能够移动和分裂。大多数模拟半柔性不可拉伸纤维/聚合物的方法基于离散（珠链或团链）模型，当考虑流体动力学时，这些模型在细长极限下变得极其昂贵。在本文中，我们开发了一种新的粗粒度方法，用于模拟具有流体动力学相互作用的涨落细丝。我们的方法专为持久长度与长度相当或更大的相对刚性纤维设计，基于三个主要贡献。首先，我们使用粗的非均匀切比雪夫网格对细丝中心线进行离散化，并在此网格上制定离散约束吉布斯-玻尔兹曼平衡分布和过阻尼朗之万方程。其次，我们将细丝上每一点的流体动力学迁移率定义为沿中心线对Rotne-Prager-Yamakawa核的积分，并应用谱精度求积法精确解析流体动力学。第三，我们提出了一种新颖的中点时间积分器，能够正确捕捉过阻尼朗之万方程中出现的伊藤漂移项。我们验证了切比雪夫网格的平衡分布能很好地近似团链模型的平衡分布，并且我们的时间积分器在足够小的时间步长下能采样平衡分布。我们还研究了初始直线细丝的松弛动力学，发现仅需12个切比雪夫节点即可很好地近似动力学，同时允许的时间步长比解析的团链模拟大两个数量级。最后，我们研究了弯曲涨落如何促进半柔性纤维交联网络中的成束过程。