编织束和紧密线圈：受阻填充的手性纤维束的结构和热力学
Braided Bundles and Compact Coils: The Structure and Thermodynamics of Hexagonally-Packed, Chiral Filament Assemblies
摘要：
分子手性阻碍了丝状分子的二维组装，这一事实反映了对层状材料施加全局扭曲的一般不可能性。我们探讨的后果，这种挫折的六边形有序组装的手性细丝是{ \it有限}的横向尺寸。具体来说，我们采用了连续弹性描述的圆柱形束的细丝，使我们能够考虑最普遍的阻力和偏好手性订购的组装。我们探讨了两种不同的机制，其中手性在分子尺度上的长丝挫败组装成聚集体。在第一种情况下，细丝之间的手性相互作用赋予细丝围绕束的中心轴的整体扭转。在第二个，我们认为是固有的螺旋结构的细丝，赋予扭曲的几何中心轴。对于这两种机制，我们发现，一个分散的{ \it有限}宽度的纤维束的结晶稳定状态出现接近，但低于，散装丝凝聚点。分散束的热力学稳定性的范围是敏感的弹性成本和偏好手性长丝包装。手性细丝的自限性组装对于一大类生物分子- DNA，丝状蛋白质，病毒，细菌鞭毛-具有特殊意义，这些生物分子普遍具有手性，并且被观察到在广泛的条件下形成紧凑的束。
英文摘要：
Molecular chirality frustrates the two-dimensional assembly of filamentous molecules, a fact that reflects the generic impossibility of imposing a global twisting of layered materials. We explore the consequences of this frustration for hexagonally-ordered assemblies of chiral filaments that are {\it finite} in lateral dimension. Specifically, we employ a continuum-elastic description of cylindrical bundles of filaments, allowing us to consider the most general resistance to and preference for chiral ordering of the assembly. We explore two distinct mechanisms by which chirality at the molecular scale of the filament frustrates the assembly into aggregates. In the first, chiral interactions between filaments impart an overall twisting of filaments around the central axis of the bundle. In the second, we consider filaments that are inherently helical in structure, imparting a writhing geometry to the central axis. For both mechanisms, we find that a thermodynamically-stable state of dispersed bundles of {\it finite} width appears close to, but below, the point of bulk filament condensation. The range of thermodynamic stability of dispersed bundles is sensitive only to the elastic cost and preference for chiral filament packing. The self-limited assembly of chiral filaments has particular implications for a large class of biological molecules -- DNA, filamentous proteins, viruses, bacterial flagella -- which are universally chiral and are observed to form compact bundles under a broad range of conditions.
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