RUI: Knotting transitions in physical systems

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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.