CAREER: Entanglement of Active Polymers

职业：活性聚合物的缠结

• 批准号: 2246745
• 负责人: Eleni Panagiotou
• 金额: $ 53.78万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-05-15 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2246745&HistoricalAwards=false
• 关键词: CAREER; Entanglement; Active; Polymers

NONTECHNICAL SUMMARY This award supports theoretical, mathematical, and computational research, and education on active polymers which can drive biological function by exerting forces and changing their shape. Biological cells contain active polymers - long filamentous molecules - that can consume energy and change connectivity and architecture during the cell cycle. The PI aims to develop a method that can provide insight into the dynamic reorganization of such systems.The PI aims to investigate whether the many-chain geometry and topology of these filaments in combination with active interconnections among polymers alone can describe key elements that account for the mechanics of active matter filaments in many contexts. This research examines this hypothesis using an approach that involves mathematical ideas from the field of topology and computer simulation to obtain results that can be compared to experiments. The PI aims to use rigorous methods from mathematics to understand, model, and eventually control how polymer filaments entangle in active physical systems with biological applications. This project will lead to a better understanding of living matter and will advance the smart manufacturing of new soft glassy materials. This project also supports outreach activities, including public talks, university outreach programs, and the Challenger STEM Center, which can present aspects of the research to a potentially wide audience. Software and simulation techniques developed through this project will be shared broadly with the community. Results will be presented by the PI and her students at interdisciplinary conferences, including those organized by the PI. Additionally, the PI is strongly committed to broadening participation of underrepresented minorities and women in STEM; new courses will be developed to train interdisciplinary scientists in 21st-century mathematical tools. TECHNICAL SUMMARY Active matter is used to classify a range of physical systems that are driven out of equilibrium by the presence of ''active'' constituents that exert forces by dissipating energy. Conventional polymer physics arguments provide limited understanding of the dynamic reorganization of such systems. A challenge in the field is to connect properties of isolated filaments to properties of a collection of filaments. This relates to a big challenge in the field of entangled polymers, which is how to measure entanglement of open curves in 3-space. This project will use topology, modeling, and simulation to measure topological entanglement in active matter filaments and provide a new model for its mechanics. This research advances knowledge and breaks existing technical barriers (1) in topology by defining and studying the Jones polynomial of a collection of open curves in 3-space and in systems employing Periodic Boundary Conditions and (2) in understanding entanglement effects in materials science and biology, by providing a new model for the viscoelastic response of active matter filaments. This work is aimed to lead to predictive modeling of the behavior of such systems with the possibility of controlling their functions by judicious selection of their chemical compositions and structures, for example, by changing the number of active cross-links or the type of cross-linking motifs. This award is jointly funded through the Condensed Matter and Materials Theory Program in the Division of Materials Research, and the Topology and Mathematical Biology Programs in the Division of Mathematical Sciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项支持理论，数学和计算研究，以及活性聚合物的教育，这些聚合物可以通过施加力和改变形状来驱动生物功能。生物细胞含有活性聚合物-长丝状分子-可以在细胞周期中消耗能量并改变连接和结构。PI的目的是开发一种方法，可以提供洞察到动态重组的系统。PI的目的是调查是否多链的几何形状和拓扑结构的这些细丝结合聚合物之间的主动互连单独可以描述的关键要素，占在许多情况下的力学活性物质细丝。本研究使用涉及拓扑学和计算机模拟领域的数学思想的方法来检验这一假设，以获得可以与实验相比较的结果。PI旨在使用严格的数学方法来理解，建模并最终控制聚合物细丝如何在具有生物应用的主动物理系统中缠结。该项目将有助于更好地了解生命物质，并将推动新型软玻璃材料的智能制造。该项目还支持外展活动，包括公开讲座，大学外展计划和挑战者STEM中心，可以向潜在的广泛受众展示研究的各个方面。通过该项目开发的软件和模拟技术将与社区广泛分享。结果将由PI和她的学生在跨学科会议上展示，包括由PI组织的会议。此外，PI还致力于扩大STEM中代表性不足的少数民族和妇女的参与;将开发新课程，以培训21世纪数学工具的跨学科科学家。 活性物质用于对一系列物理系统进行分类，这些物理系统由于存在通过耗散能量施加力的“活性"成分而被驱离平衡。传统的聚合物物理参数提供了有限的理解动态重组这样的系统。该领域的一个挑战是将孤立细丝的性质与细丝集合的性质联系起来。这涉及到纠缠聚合物领域的一大挑战，即如何测量三维空间中开放曲线的纠缠度。这个项目将使用拓扑学、建模和模拟来测量活性物质细丝中的拓扑纠缠，并为其力学提供新的模型。 本研究通过定义和研究三维空间和采用周期性边界条件的系统中的开放曲线集合的琼斯多项式来推进知识并打破现有的技术障碍（1）拓扑学和（2）理解材料科学和生物学中的纠缠效应，通过提供活性物质细丝的粘弹性响应的新模型。这项工作的目的是导致这些系统的行为的预测建模，通过明智地选择它们的化学组成和结构，例如，通过改变活性交联的数量或交联基序的类型来控制它们的功能。 该奖项由材料研究部的凝聚态物质和材料理论项目以及数学科学部的拓扑学和数学生物学项目共同资助。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。