CAREER: Entanglement of Active Polymers

职业：活性聚合物的缠结

• 批准号: 2047587
• 负责人: Eleni Panagiotou
• 金额: $ 53.78万
• 依托单位: University of Tennessee Chattanooga
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-08-15 至 2023-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2047587&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.

非技术概述该奖项支持有关活性聚合物的理论、数学和计算研究以及教育，这种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--在细胞周期中会消耗能量并改变连接性和结构。PI的目的是开发一种方法来洞察这类系统的动态重组。PI的目的是调查这些细丝的多链几何和拓扑结构以及聚合物之间的活性互连是否能够描述在许多情况下解释活性物质细丝的机制的关键元素。这项研究使用了一种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的目标是使用数学中的严格方法来理解、建模并最终控制聚合物细丝如何在具有生物应用的活动物理系统中缠绕。该项目将有助于更好地了解生物，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，包括公开演讲、大学外展计划和挑战者STEM中心，这些活动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广泛与社区共享。结果将由国际和平协会和她的学生在跨学科会议上公布，包括由国际和平协会组织的会议。此外，非政府组织坚定地致力于扩大代表不足的少数群体和妇女在STEM中的参与；将开发新的课程，以培训跨学科科学家掌握21世纪的数学工具。技术概述活性物质被用来对一系列物理系统进行分类，这些物理系统是由于存在通过耗散能量而施加力的“活性”成分而被驱离平衡的。传统的聚合物物理争论对此类系统的动态重组提供了有限的理解。该领域的一个挑战是将孤立细丝的特性与细丝集合的特性联系起来。这涉及到纠缠聚合物领域的一大挑战，即如何在三维空间中测量开放曲线的纠缠。本项目将利用拓扑学、建模和模拟技术来测量活性物质细丝中的拓扑纠缠，并为其力学提供一个新的模型。本研究通过定义和研究三维空间和周期边界条件系统中一组开放曲线的Jones多项式，突破了现有的技术障碍：(1)在拓扑学方面，通过定义和研究周期边界条件下的一组开放曲线的Jones多项式；(2)在理解材料科学和生物学中的纠缠效应方面，通过为活性物质细丝的粘弹性响应提供新的模型。这项工作的目的是对这类系统的行为进行预测建模，并有可能通过明智地选择其化学成分和结构来控制其功能，例如通过改变活性交联链的数量或交联基序的类型。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智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

A computational package for measuring Topological Entanglement in Polymers, Proteins and Periodic systems (TEPPP)

• DOI: 10.1016/j.cpc.2022.108639
• 发表时间: 2023-01-24
• 期刊: COMPUTER PHYSICS COMMUNICATIONS
• 影响因子: 6.3
• 作者: Herschberg, Tom;Pifer, Kyle;Panagiotou, Eleni
• 通讯作者: Panagiotou, Eleni

The Jones polynomial of collections of open curves in 3-space

3 空间中开曲线集合的琼斯多项式

• DOI: 10.1098/rspa.2022.0302
• 发表时间: 2022
• 期刊: Physical and Engineering Sciences
• 作者: Barkataki, Kasturi;Panagiotou, Eleni
• 通讯作者: Panagiotou, Eleni

The second Vassiliev measure of uniform random walks and polygons in confined space

有限空间中均匀随机游走和多边形的第二个 Vassiliev 测度

• DOI: 10.1088/1751-8121/ac4abf
• 发表时间: 2022
• 期刊: Journal of Physics A: Mathematical and Theoretical
• 作者: Smith, Philip;Panagiotou, Eleni
• 通讯作者: Panagiotou, Eleni