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-2015-03747
• 负责人: Soteros, Christine
• 金额: $ 1.6万
• 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: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=589350
• 关键词: Lattice; Models; Polymers; Entanglement; Complexity

The lattice models of Statistical Mechanics have proved to be powerful tools for studying phase-change behaviour and equilibrium properties for polymers in solution. For such models, a polymer is considered to be any long chain molecule made of repeated units called monomers and 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. 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 a highly simplified model, it is useful for predicting and understanding  phenomena that result from the fact that polymers are large flexible molecules. 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 by us. At the same time, there is interest in understanding the entanglement complexity of polymers confined in pores or capsids (such as DNA in a viral capsid) and also interest in determining the role of entanglements in polymer crystallization and polymer melts. For example, there are open questions about the relationship between how a polymer is packed in a capsid and its entanglement complexity, and for polymer melts, about the best approach for measuring the extent of entanglement. Lattice models for investigating these questions have also been developed by us. 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. The results 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. More generally, the results will add to our overall understanding of lattice models of polymers and phase transitions in polymer systems.

统计力学的格子模型已被证明是研究溶液中聚合物相变行为和平衡性质的有力工具。 对于这样的模型，聚合物被认为是由称为单体的重复单元组成的任何长链分子，并且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。所得的晶格聚合物具有柔性（它可以呈现各种形状），并且容易结合两个单体不能处于相同位置（排除体积效应）的要求。 虽然这是一个高度简化的模型，但它对于预测和理解聚合物是大的柔性分子这一事实所导致的现象是有用的。 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，一个模型，其中一个晶格聚合物链的两端连接成一个环，可以用来代表DNA分子的大规模结构，和模型的酶作用于DNA已经开发了我们。 在同一时间，有兴趣在理解的缠结复杂性的聚合物限制在孔或衣壳（如DNA在病毒衣壳），也有兴趣在确定的作用缠结在聚合物结晶和聚合物熔体。例如，关于聚合物如何包装在衣壳中与其缠结复杂性之间的关系，以及对于聚合物熔体，关于测量缠结程度的最佳方法，存在公开的问题。我们还开发了用于调查这些问题的格模型。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。 这些结果将引起分子生物学家和高分子化学家的兴趣。 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。更一般地说，结果将增加我们的整体理解的晶格模型的聚合物和聚合物体系中的相变。