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: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=521807
• 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.

聚合物是由被称为单体的重复分子单元组成的任何大分子。统计力学的晶格模型已被证明是研究聚合物在溶液中的相变行为和平衡性质的简单而有力的方法。为此，聚合物链由格子或晶格上的行走来表示，因此链中的每个单体都与其相邻的单体相距一步。有利的是，得到的晶格聚合物具有很大的柔韧性(它可以呈现各种形状)，并且两个单体不能在同一位置的要求(排除的体积效应)很容易合并。尽管高度简化，但对于预测和理解主要是由于聚合物是由重复单元组成的大的柔性分子这一事实而产生的任何性质，它是一个有用的模型。与此同时，这些模型具有内在的数学兴趣，因为有大量具有挑战性的开放数学问题，其中许多来自聚合物物理，最近来自分子生物学，与它们有关。例如，酶作用于环状生物聚合物，如环状DNA，以消除DNA的缠结，以便正常的细胞过程进行。为了研究这一点，一个晶格聚合物链的两端连接成一个环的模型可以用来表示DNA分子的大尺度结构，而一个酶对结果环的作用模型正在开发中。与此同时，聚合物化学家对确定缠结在聚合物结晶和聚合物熔体中的作用很感兴趣。然而，对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。我计划利用组合分析和计算机模拟继续我对聚合物晶格模型的研究，以便更好地理解酶对DNA的作用，并确定好的纠缠复杂性衡量标准。这一结果将引起分子生物学家和聚合物化学家的兴趣。同时，这些结果将增加我们对聚合物的晶格模型和聚合物体系中的相变的一般理解。