Folding and Unfolding of Polygonal Linkages, with Applications to Structural Biology

多边形连接的折叠和展开及其在结构生物学中的应用

• 批准号: 0310661
• 负责人: Ileana Streinu
• 金额: $ 65万
• 依托单位: Smith College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0310661&HistoricalAwards=false
• 关键词: Folding; Unfolding; Polygonal; Linkages; Applications

ABSTRACTWe are studying folding and unfolding processes for polygonal linkages (and other partially rigid structures with many degrees of freedom) in dimensions two and three, with particular emphasis on applications in molecular biology. Our primary focus is on fundamental mathematical properties (topologic, geometric, algebraic) and novel algorithmic approaches, with the long run goal of understanding the fundamental laws of the protein folding simulation problem. We are proposing a novel Monte Carlo approach for move generators in energy minimization simulations in two dimensions, based on mechanisms which simultaneously change many angles and are guaranteed to be collision free, and we investigate the feasibility of extending the approach in three dimensions. The mathematics involved in this research includes techniques from algebraic topology, algebraic geometry and rigidity theory, while the computational effort is expected to lead to developing efficient data structures and algorithms for planning, analyzing, approximating, and tracking such motions. Besides its intrinsic scientific merit, we anticipate this project to have broader impact through a novel way of integrating research, teaching, inter-institutional and interdisciplinary collaborations. The grant will allow one of the PIs, who teaches at the undergraduate level at a women's college, to establish an integrated research group including (besides undergraduates) graduate students. By bringing top research resources and powerful collaborations to an undergraduate institution devoted to promoting the technical education of women in a liberal arts environment, we expect to influence the interdisciplinary curriculum of the future, enhance the infrastructure for research and education at the only women's college with an engineering program, and generate models for training a diverse body of students for graduate work, research and teaching.

摘要我们正在研究二维和三维多边形连接（以及其他具有多个自由度的部分刚性结构）的折叠和展开过程，特别强调在分子生物学中的应用。我们的主要重点是基本数学特性（拓扑、几何、代数）和新颖的算法方法，长期目标是理解蛋白质折叠模拟问题的基本规律。我们提出了一种新颖的蒙特卡罗方法，用于二维能量最小化模拟中的移动发电机，该方法基于同时改变多个角度并保证无碰撞的机制，并且我们研究了在三个维度上扩展该方法的可行性。这项研究涉及的数学包括代数拓扑、代数几何和刚性理论的技术，而计算工作预计将导致开发有效的数据结构和算法，用于规划、分析、近似和跟踪此类运动。除了其内在的科学价值外，我们预计该项目将通过一种整合研究、教学、机构间和跨学科合作的新颖方式产生更广泛的影响。这笔赠款将允许一名在女子学院教授本科生的 PI 建立一个综合研究小组，其中包括（除本科生外）研究生。通过为一所致力于在文科环境中促进女性技术教育的本科院校带来顶尖的研究资源和强有力的合作，我们期望影响未来的跨学科课程，加强唯一女子学院的研究和教育基础设施一个工程项目，并生成模型来培训不同的学生群体进行研究生工作、研究和教学。