Lattice models of polymers: entanglement complexity and phase transitions

聚合物晶格模型：纠缠复杂性和相变

• 批准号: 46659-2010
• 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: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=507334
• 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 alot of 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 a useful model for predicting and understanding any properties which are mainly a consequence of the fact that a polymer is a large flexible molecule made up of repeated units. 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, concerning them. For example, enzymes act on ring-like biopolymers such as circular DNA to remove entanglements from DNA 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 a model of enzyme action on the resulting ring is in development. At the same time, polymer chemists are interested in determining the role of entanglements in polymer crystallization and polymer melts. It is an open question, however, as to the best approach for measuring the extent of entanglement. A model for investigating entanglement measures has also 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 determine good measures of entanglement complexity. The results will be of interest to molecular biologists and polymer chemists. At the same time, the results will add to our general understanding of lattice models of polymers and phase transitions in polymer systems.

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大量的柔性（其可以呈现各种形状）并且容易地结合两个单体不能处于相同位置（排除体积效应）的要求。 虽然高度简化，它是一个有用的模型，用于预测和理解任何性质，这主要是一个事实的结果，即聚合物是一个大的灵活的分子组成的重复单元。 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，其中许多已经出现从聚合物物理学和最近从分子生物学，关于他们。 例如，酶作用于环状生物聚合物，如环状DNA，以去除DNA的缠结，以便进行正常的细胞过程。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，和酶作用于所产生的环的模型正在开发中。 与此同时，高分子化学家对确定缠结在聚合物结晶和聚合物熔体中的作用感兴趣。 然而，关于测量纠缠程度的最佳方法，这是一个悬而未决的问题。 还开发了一个用于研究纠缠措施的模型。我计划使用组合分析和计算机模拟继续研究聚合物的晶格模型，以便更好地了解酶对DNA的作用，并确定纠缠复杂性的良好措施。 这些结果将引起分子生物学家和高分子化学家的兴趣。 同时，这些结果将有助于我们对高分子晶格模型和高分子体系相变的理解。