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无处不在。这些物体可以缠绕在一起，并在不同类型的结之间转换。有时大自然需要消除这种打结，比如当II型拓扑异构酶切割并重新连接DNA链以释放复制过程中的相互连接时。这些II型拓扑异构酶是一些化疗药物以及用于治疗炭疽中毒的抗生素环丙沙星的靶标。在其他时候，打结是为了某种目的而产生的，比如在一些蛋白质折叠成其功能性打结的天然状态时。虽然这些蛋白质中打结的确切功能尚不清楚，但确定其功能可以使操纵蛋白质或设计用于医疗应用的新蛋白质成为可能。在其他时候，打结的变化是自然老化的产物。例如，当亚原子胶球粒子在其生命周期中衰变时，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过程，不同类型结之间的转换揭示了物理系统的特性。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。几名本科生将直接获得资助。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。学生将参加专业会议，并在讲座和海报中传播他们的发现。这些研究经验对于培养下一代科学和数学教育工作者、研究人员和实践者至关重要。为了获得更广泛的受众，PI将继续积极地为学生、非专业人士和多学科受众做报告。研究结果将发表在数学和科学期刊上。PI将组织跨学科会议，将传统上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，研究成果、数据和软件将通过万维网公开提供。虽然传统上对打结的数学研究主要集中在闭合环上，但自然界中的打结大多发生在具有自由末端（即开链）的物体上。该项目将建立对开放结结构的牢固理解，包括开链和闭环内的结子结构。这些知识将用于对蛋白质中的打结进行分类，并且数据将公开提供。在结蛋白中确定结、几何结构和氨基酸序列之间的关系，以确定结在结蛋白中的功能。由于II型拓扑异构酶的作用，建模打结转变将导致更好地理解他们在解开DNA链的有效性。类似的分析将用于确定亚原子胶球如何通过打结而衰变。总之，这些项目将揭示自然界打结的基本见解。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)揭示结蛋白中结的功能；3)确定II型拓扑异构酶在哪里执行切割和重新连接作用；4)了解胶球的衰变过程。新的和建立的模型和计算机应用程序的组合将用于分析这些物理系统。除了科学目标外，该项目还有广泛的教育目标。几名本科生将直接获得资助。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。学生将参加专业会议，并在讲座和海报中传播他们的发现。这些研究经验对于培养下一代科学和数学教育工作者、研究人员和实践者至关重要。为了获得更广泛的受众，PI将继续积极地为学生、非专业人士和多学科受众做报告。研究结果将发表在数学和科学期刊上。PI将组织跨学科会议，将传统上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，研究成果、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.