RUI: Knotting transitions in physical systems

从微小的DNA到巨大的太阳耀斑，弦状物体在自然界中以各种尺度充满。这些对象可以在不同类型的结之间纠缠和过渡。有时，大自然需要消除这种打结，例如当被称为II型拓扑异构酶的酶切割并重新连接DNA链以在复制过程中释放链接时。这些II型拓扑异构酶是一些化疗药物的靶标，也是用于治疗炭疽中毒的抗生素Cipro的靶标。在其他时候，打结是为了某个目的而产生的，例如在某些蛋白质折叠成其功能打结的自然状态时。虽然这些蛋白质中打结的确切功能尚不清楚，但确定其功能可能使操纵蛋白质或设计用于医疗应用的新蛋白质成为可能。还有一些时候，打结的变化是自然退化的产物。例如，随着亚原子胶球粒子在其生命周期中衰变，它们会在不同类型的结之间变化。事实上，自然界中的打结是一个动态的过程，不同类型的打结之间的转换揭示了物理系统的属性。在这个项目中，PI，一个多学科的合作者小组，和本科生研究拓扑异构酶II、蛋白质和胶球的打结转变，以深入了解打结在这些系统中的作用。这个项目有广泛的教育目标。几名本科生将直接得到这笔助学金的支持。他们将接受PI的培训，并为项目做出贡献，在研究过程中获得内容知识和经验。学生们将参加专业会议，并通过演讲和海报传播他们的发现。这些研究经验对于培训下一代科学和数学教育者、研究人员和实践者至关重要。为了接触到广泛的受众，PI将继续积极向学生、非专业人士和跨学科的受众进行演讲。研究结果将发表在数学和科学期刊上。国际和平研究所将组织跨学科会议，将来自传统不同领域的科学家聚集在一起，并与世界各地的研究人员建立新的跨学科合作。此外，作为这项拨款的一部分而产生的研究结果、数据和软件将通过万维网公开。虽然打结的数学研究传统上集中在闭合环上，但自然界中的许多打结发生在具有自由端的物体(即开链)中。这个项目将建立对开放打结结构的坚定理解，包括开链和闭合环内的打结子结构。这些知识将被用于对蛋白质中的打结进行分类，并将公开数据。将确定打结蛋白质中的打结、几何结构和氨基酸序列之间的关系，以确定打结蛋白质中打结的功能。对由II型拓扑异构酶的作用引起的打结转变进行建模将有助于更好地理解它们在解开DNA链方面的有效性。一个类似的分析将被用来确定亚原子胶球如何通过打结衰变。总之，这些项目将揭示对自然界中打结的基本见解。更具体地说，这项资助的主要目标是1)将复杂的结分解成它们的基本元素，2)揭示打结蛋白质中打结的功能，3)确定II型拓扑异构酶在哪里进行切割和再连接作用，以及4)了解胶球中的衰变过程。将使用新的和已建立的模型以及计算机应用程序相结合来分析这些物理系统。除了科学目标外，这个项目还有广泛的教育目标。几名本科生将直接得到这笔助学金的支持。他们将接受PI的培训，并为项目做出贡献，在研究过程中获得内容知识和经验。学生们将参加专业会议，并通过演讲和海报传播他们的发现。这些研究经验对于培训下一代科学和数学教育者、研究人员和实践者至关重要。为了接触到广泛的受众，PI将继续积极向学生、非专业人士和跨学科的受众进行演讲。研究结果将发表在数学和科学期刊上。国际和平研究所将组织跨学科会议，将来自传统不同领域的科学家聚集在一起，并与世界各地的研究人员建立新的跨学科合作。此外，作为这笔赠款的一部分产生的研究结果、数据和软件将通过万维网公开提供。

From microscopic DNA to massive solar flares, string-like objects are replete in nature at every scale. These objects can be entangled and transition between different types of knots. Sometimes nature needs to eliminate this knotting, such as when enzymes called type II topoisomerases cut and reattach strands of DNA to release interlinking during replication. These type II topoisomerases are targets for some chemotherapy drugs, as well as the antibiotic Cipro which is used to treat anthrax poisoning. At other times, knotting is created for a purpose, such as in the folding of some proteins into their functional knotted native state. While the exact function of the knotting in these proteins is unknown, determining the function could make it possible to manipulate proteins or design new proteins for medical applications. At still other times, changes in knotting are the product of natural deterioration. For example, as sub-atomic glueball particles decay through their lifetimes, they change between different types of knots. Indeed, knotting in nature is a dynamic process and the transitions between different types of knots reveal properties of the physical systems. In this project, the PI, a multi-disciplinary group of collaborators, and undergraduate students study knotting transitions for topoisomerase II, proteins, and glueballs to gain insights into the role of knotting in these systems. This project has broad educational objectives. Several undergraduate students will be supported directly by the grant. They will be trained by the PI and contribute to the projects, gaining both content knowledge and experience in the research process. The students will participate in professional meetings and disseminate their findings in talks and posters. These research experiences are essential in training the next generation of science and mathematics educators, researchers, and practitioners. To reach a wide-audience, the PI will continue to be active in giving presentations to students, non-specialists, and multi-disciplinary audiences. The results will be published in mathematics and science journals. The PI will organize interdisciplinary conference sessions to bring together scientists from traditionally disparate fields and create new interdisciplinary collaborations with researchers across the world. In addition, the research results, data, and software generated as a part of this grant will be made publicly available via the world wide web.While the mathematical study of knotting has focused traditionally on closed loops, much of the knotting in nature occurs in objects with free ends (i.e. open chains). This project will establish a firm understanding of open knotted structures, including knotted substructures within open chains and closed loops. This knowledge will be applied to classify the knotting in proteins and the data will be made publicly available. Relationships between knotting, geometric structure, and the amino acid sequence in knotted proteins will be determined to establish the function of the knotting in knotted proteins. Modeling knotting transitions due to the action of type II topoisomerases will lead to a better understanding of their effectiveness in untangling DNA strands. A similar analysis will be used to determine how subatomic glueballs decay through knotting. Together, these projects will reveal fundamental insights into knotting in nature. More specifically, the main objectives of this grant are to 1) decompose complicated knots into their essential elements, 2) reveal the function of knotting in knotted proteins, 3) determine where type II topoisomerases perform their cutting and reattaching action, and 4) understand the decaying process in glueballs. A combination of new and established models and computer applications will be used to analyze these physical systems. In addition to the scientific goals, this project has broad educational objectives. Several undergraduate students will be supported directly by the grant. They will be trained by the PI and contribute to the projects, gaining both content knowledge and experience in the research process. The students will participate in professional meetings and disseminate their findings in talks and posters. These research experiences are essential in training the next generation of science and mathematics educators, researchers, and practitioners. To reach a wide-audience, the PI will continue to be active in giving presentations to students, non-specialists, and multi-disciplinary audiences. The results will be published in mathematics and science journals. The PI will organize interdisciplinary conference sessions to bring together scientists from traditionally disparate fields and create new interdisciplinary collaborations with researchers across the world. In addition, the research results, data, and software generated as a part of this grant will be made publicly available via the world wide web.