RUI: Structure of Entanglement in Macromolecules

紧密缠结管的结构已被用来预测缠结大分子的性质，例如蛋白质中α螺旋的螺距和DNA双螺旋的螺距。此外，物理学家提出，被称为胶球的亚原子粒子是紧密纠缠在一起的QCD通量管。虽然在数学和科学上对这些紧密纠缠有很大的兴趣，但除了一些简单的例子外，对所有这些纠缠的明确描述都是未知的。在该项目的第一部分，项目负责人、合作者和学生们通过仔细的数值模拟来确定紧密结和连接的结构，并使用数据来明确描述紧密配置及其管对管接触集。这些结构提供了对长管如何装入小空间的见解，以及在自然界中可以看到的行为（例如在病毒衣壳中DNA的包装）。在形成开链的天然材料中也可以看到缠结现象。例如，聚合物链中纠缠区域的存在（或不存在）引发了许多关于结构和功能之间复杂相互作用的有趣问题。最近，蛋白质中打结区域的发现受到了广泛的关注。然而，检测区域的算法（因此，确切地定义一个结开链是什么）因研究小组而异，非常需要严格的分析。在这个项目的第二部分，PI，合作者和学生探索开链打结的新概念，可以用来检测聚合物中的纠缠区域，然后测量这些打结区域的大小和形状。特别是，他们对开链中的缠结建立了坚实的理论认识，使用新的和已建立的空间测量来更好地理解连接的链链和结的聚合物链和环的形状，并找到聚合物模型结构与紧结结构之间的联系。打结和缠结在自然界的任何尺度上都经常发生。例如，DNA在生物反应中形成结，物理学家推测太阳风暴期间形成的磁场可以打结。开尔文早期提出的基本粒子形成结的理论，最近在亚原子粒子胶球的研究中得到了支持。胶球被假设成紧密纠缠在一起的管子形状。其他链状的天然物质也可以紧密地包裹在一起，例如，大量的DNA被包裹在病毒的头部，DNA释放到细胞中是感染过程的先头。这些链的结构和功能本质上是交织在一起的。特别是，了解这些链的天然结构是操纵过程的关键一步，例如制造设计塑料或识别和杀死流氓细胞。PI、合作者和学生们研究了两种模型：紧实现的结和发生在开放链和封闭链中的结。应用实例包括预测未识别的胶球，描述材料如何在小空间内紧密堆积，以及描述蛋白质开放链中结的结构。

The structures of tightly entangled tubes have been used to predict properties of entangled macromolecules, e.g. the pitch of alpha helices in proteins and the pitch of the DNA double helix. In addition, physicists have proposed that subatomic particles known as glueballs are tightly entangled QCD flux tubes. While there is a great deal of mathematical and scientific interest in these tight entanglements, explicit descriptions are unknown for all but some simple examples. In the first portion of this project, the PI, collaborators, and students determine the structure of tight knots and links by performing careful numerical simulations and using the data to provide explicit descriptions of tight configurations and their sets of tube-to-tube contacts. These configurations provide insights into how long tubes pack into small spaces, behavior seen throughout nature (e.g. in the packing of DNA in viral capsids). Entanglement can also be seen in natural materials that form open chains. The existence (or lack thereof) of entangled regions in polymeric chains, for example, raises many interesting questions regarding the complex interplay between structure and function. Recently, the discovery of knotted regions in proteins has received much attention. However, the algorithms for detecting the regions (and, thus, the definition of exactly what a knotted open chain is) vary by research group and is in much need of rigorous analysis. In the second portion of this project, the PI, collaborators, and students explore new notions of knotting in open chains that can be used to detect entangled regions in polymers and then measure the size and shape of these knotted regions. In particular, they establish a firm theoretical understanding of entanglement in open chains, use new and established spatial measurements to better understand the shapes of linked catenanes and knotted polymer chains and loops, and find connections between the structure of polymer models and those of tight knots.Knotting and tangling occur frequently in nature at every scale. For example, DNA forms knots during biological reactions and physicists conjecture that magnetic fields formed during storms on the sun can be knotted. The early proposal of Kelvin that elementary particles form knots found recent support in studies of subatomic particles known as glueballs which are hypothesized to take the shape of tightly entangled tubes. Other chain-like natural materials pack tightly as well, e.g. a large amount of DNA is packed into the head of viruses and the release of the DNA into the cell is what spearheads the infection process. The structure and function of these chains are inherently intertwined. In particular, understanding the native structure of these chains is a key step in manipulating processes, such as in creating designer plastics or identifying and killing rogue cells. The PI, collaborators, and students study two models: tight realizations of knots and knots occurring in open and closed chains.Examples of applications include predicting unidentified glueballs, describing how materials pack tightly in small spaces, and characterizing the structure of knots in open chains of protein.