Lattice Models of Polymers: Entanglement Complexity and Confined Geometries

聚合物的晶格模型：纠缠复杂性和受限几何形状

• 批准号: RGPIN-2020-06339
• 负责人: Soteros, Christine
• 金额: $ 1.75万
• 依托单位: University of Saskatchewan
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=740756
• 关键词: Lattice; Models; Polymers; Entanglement; Complexity

A polymer is any large molecule made up of repeated molecular units called monomers. The lattice models of Statistical Mechanics have proved to be simple but powerful for studying phase-change behaviour and equilibrium properties for polymers in solution. For this, a polymer chain is represented by a walk on a grid or lattice so that each monomer in the chain is one step apart from its neighbours. Advantageously, the resulting lattice polymer has flexibility (it can take on a variety of shapes) and the requirement that two monomers cannot be in the same location (the excluded volume effect) is easily incorporated. Although highly simplified, it is useful for predicting and understanding any properties which are a consequence of the fact that a polymer is a large flexible molecule. At the same time, these models are of intrinsic mathematical interest due to the wealth of challenging open mathematical questions, many of which have arisen from polymer physics and more recently from molecular biology. For example, enzymes act on DNA to remove entanglements in order for normal cellular processes to proceed. To study this, a model in which two ends of a lattice polymer chain are joined into a ring can be used to represent the large-scale structure of the DNA molecule, and models of enzyme action on DNA have been developed. At the same time, there is interest in understanding the entanglement complexity of polymers confined in nanochannels or capsids (such as DNA in a viral capsid) or when stretched as in single-molecule atomic force microscopy experiments. There are open questions for all these cases regarding the connection between how the polymer is stretched or packed and its entanglement complexity. Lattice models for investigating these questions have been developed. I plan to continue my research on lattice models of polymers using combinatorial analysis and computer simulations in order to better understand enzyme action on DNA and the entanglement complexity of confined polymers. In doing so, I am committed to promoting equity, diversity, and inclusion in my research program. I am aware that women and minorities are historically underrepresented in the sciences and will therefore encourage applications from women, members of visible minorities, indigenous persons, and persons with disabilities to join my research team. The results of this research program will be of interest to molecular biologists and polymer chemists. In the case of enzyme action on DNA, an improved understanding of their action has the potential to impact Canadians by leading to improved cancer treatments. At the same time, the results will add to our general understanding of lattice models of polymers and phase transitions in polymer systems.  Trainees involved in the research program will benefit from the development of critical thinking and problem-solving abilities, as well as technical, collaborative and communication skills.

聚合物是由称为单体的重复分子单元组成的任何大分子。统计力学的格子模型已被证明是简单而强大的研究相变行为和平衡性质的聚合物在溶液中。为此，聚合物链由网格或晶格上的行走表示，使得链中的每个单体与其相邻单体相距一步。有利地，所得的晶格聚合物具有柔性（其可以呈现各种形状）并且容易地结合两种单体不能处于相同位置（排除体积效应）的要求。虽然高度简化，它是有用的预测和理解任何性质的结果，聚合物是一个大的灵活的分子。与此同时，这些模型是内在的数学兴趣，由于丰富的具有挑战性的开放的数学问题，其中许多已经出现在聚合物物理学和最近从分子生物学。例如，酶作用于DNA以去除缠结，以便正常的细胞过程进行。为了研究这一点，可以使用晶格聚合物链的两端连接成环的模型来表示DNA分子的大尺度结构，并且已经开发了酶作用于DNA的模型。与此同时，人们有兴趣了解限制在纳米通道或衣壳（如病毒衣壳中的DNA）中的聚合物的缠结复杂性，或者在单分子原子力显微镜实验中拉伸时的缠结复杂性。对于所有这些情况，关于聚合物如何被拉伸或包装与其纠缠复杂性之间的联系，都存在悬而未决的问题。研究这些问题的格子模型已经被开发出来。 我计划继续使用组合分析和计算机模拟对聚合物的晶格模型进行研究，以便更好地了解酶对DNA的作用和受限聚合物的纠缠复杂性。在这样做的时候，我致力于促进公平，多样性和包容性在我的研究计划。我知道，妇女和少数民族在科学领域的代表性历来不足，因此，我将鼓励妇女、明显少数民族成员、土著人和残疾人申请加入我的研究团队。该研究计划的结果将引起分子生物学家和聚合物化学家的兴趣。在酶对DNA的作用的情况下，对其作用的更好理解有可能通过改善癌症治疗来影响加拿大人。同时，研究结果将增加我们对聚合物晶格模型和聚合物体系相变的总体理解。参与研究计划的学员将受益于批判性思维和解决问题能力的发展，以及技术，协作和沟通技能。