In this work, we present a computational formulation based on continuum mechanics to study the interaction of fluid membranes embedded with semiflexible filaments. This is motivated by systems in membrane biology, such as cytoskeletal networks and protein filaments aiding the cell fission process. We model the membrane as a fluid shell via the Helfrich-Canham energy and the filament as a one-dimensional Cosserat continuum. We assume the filament to be tethered to the surface of the membrane in a way that it is allowed to float on the surface freely. The novel filament-membrane coupling, which is anticipated to yield interesting physics, also gives rise to unique computational challenges, which we address in this work. We present validation results and apply the formulation to certain problems inspired by cellular biology.

翻译：本工作基于连续介质力学提出了一种计算框架，用于研究嵌入半柔性细丝的流体膜相互作用。该研究的动机源于膜生物学中的系统，例如细胞骨架网络及辅助细胞分裂过程的蛋白质细丝。我们通过Helfrich-Canham能量将膜建模为流体壳，并将细丝建模为一维Cosserat连续介质。我们假设细丝以可自由浮动的形式系缚于膜表面。这种新颖的细丝-膜耦合机制预计将产生有趣的物理现象，同时也带来了独特的计算挑战，本文针对这些挑战进行了解决。我们展示了验证结果，并将该框架应用于若干受细胞生物学启发的典型问题。