Phase behavior and structure of semiflexible polymers in spherical confinement

半柔性生物聚合物，如核酸（例如DNA）和蛋白质，可以在足够高的浓度下自组装成具有有序排列的液晶。这些系统表现出广泛的结构和功能特性，这是关于形态发生和生物体的进化，以及为biomedical application.To阐明这些复杂的系统的行为的问题的根本利益，我们研究了模型系统的半柔性链的溶致溶液中的约束下，使用分子动力学（MD）模拟和密度泛函理论（DFT）计算。为了涵盖长度尺度的代表性范围（实际上，衣壳和囊泡的半径在10 nm和50µm之间变化），我们专注于两种极限情况，即球形限制，其中球体半径与链（或持久性）长度相当，以及平面限制，对应于无限大的半径。在这里，我们研究了纯粹的排斥和吸引力壁聚合物相互作用。对于强吸引力，我们确定了新的有序状态的墙壁，类似于液晶的“近晶C”的安排。当曲率半径是可比的链长，我们发现了一个薄的向列有序层的聚合物在限制膜的拓扑缺陷与“网球”或双极纹理。随着聚合物浓度的增加，我们发现球内和球表面的局域有序性之间存在着非平凡的竞争，为了使这种现象合理化，还需要详细研究该模型在体相中的有序态和相变。到目前为止，我们发现标准理论（基于蠕虫状链模型结合第二维里系数）是不准确的，由于持久长度和链直径之间的比率的非平凡作用。这一发现激发了Egorov教授（Escherina）和Doyle教授（Oxford）为这些系统开发两种新版本的DFT。然而，尽管这些理论有所改进，但它们不能描述集体弯曲波动的出现（在所谓的偏转长度的尺度上）。由于对于上面列出的许多应用，细胞或囊泡的限制表面的弹性变形是相关的，因此现在也将非刚性但可变形的限制膜包括在研究中。还将研究相关液晶相的弹性性质。最后，将研究在约束条件下的有序和相分离之间的相互作用。

Semiflexible biopolymers, such as nucleic acids (e.g. DNA) and proteins, can self-assemble into liquid crystals with nematic ordering at sufficiently high concentrations. These systems exhibit a wide range of structural and functional properties, which are of fundamental interest for questions regarding morphogenesis and the evolution of living organisms, as well as for biomedical applications.To elucidate the behavior of these complex systems, we studied model systems of semiflexible chains in lyotropic solution under confinement using molecular dynamics (MD) simulations and density functional theory (DFT) calculations. To cover a representative range of length scales (in practice, radii of capsids and vesicles vary between 10nm and 50µm), we focused on two limiting cases, i.e. spherical confinement where the sphere radii are comparable to the chain (or persistence) length, as well as planar confinement, corresponding to infinitely large radii. Here, we investigated both purely repulsive and attractive wall-polymer interactions. For strong attractions, we identified novel ordered states at the walls, resembling a liquid-crystalline "smectic C" arrangement. When the radius of curvature was comparable to the chain length, we found a thin nematically ordered layer of polymers at the confining membrane with topological defects with a "tennis-ball" or bipolar texture. As the polymer concentration was increased, we found a non-trivial competition between the local ordering in the interior and on the surface of the sphere.In order to rationalize these phenomena, it is also required to study in detail the ordered states and phase transitions of this model in the bulk. So far, we found that the standard theory (based on the wormlike chain model in combination with the second virial coefficient) is inaccurate, due to the non-trivial role of the ratio between the persistence length and chain diameter. This finding has motivated the development of two new versions of DFT for these systems by Prof. Egorov (Virgina) and by Prof. Doyle (Oxford). However, despite their improvements, these theories cannot describe the emergence of collective bending fluctuations (on the scale of the so-called deflection length). Since for many of the applications listed above elastic deformation of the confining surface of the cell or vesicle is relevant, now also confining membranes that are not rigid but deformable will be included in the study. Also elastic properties of the relevant liquid-crystalline phases will be studied. Finally, the interplay between nematic order and phase separation under confinement will be investigated.