Computer simulation of confined polymers and 2D catenated-ring networks

聚合物是柔性的链状分子，在自然界中无处不在。 DNA是一种特别重要的具有生物相关性的聚合物，其核苷酸序列包含生物体的遗传蓝图。近年来，有大量的研究活动集中在开发用于操纵和表征DNA的物理性质的新技术上。这些“纳米流体”技术中的许多技术涉及将DNA运输到非常紧凑的空间区域。已知聚合物在这些区域中的限制会影响它们的物理性质，理解这一点对于合理设计DNA分析装置以及理解细菌中的染色体分离等生物现象是必不可少的。DNA可以以外来形式存在于某些生物体中。例如，动质体是在锥虫寄生虫的线粒体中发现的结构，其由二维“锁子甲”膜中的数千个互锁的DNA环组成。最近的实验已经描述了这些物体的一些独特性质，它们的行为就像热化的弹性膜。动塑体可以作为开发具有技术应用的新型二维材料的灵感来源。 我将使用计算机模拟方法来模拟最近实验中研究的DNA系统。仿真是在计算机上对模型系统进行的虚拟实验。仿真可以用来解释实验结果，并测试实验系统的理论描述的有效性。模拟将采用非常简单的分子模型，以使计算可行。我将集中讨论两个广泛的主题。首先，我将使用2D网络的联锁硬环模型动塑体。我将讨论以下问题：（1）动质体凹形的物理起源是什么？(2)动基体DNA的柔性、溶剂条件、穿孔的存在以及连接拓扑结构对膜的平均大小和形状有什么影响？ 第二个主题集中在一个或两个聚合物系统的限制效应。我将解决以下问题：（1）约束如何影响组织和动力学的两个强约束聚合物在类似的条件下，最近在DNA纳米流体实验检查？(2)明确计算的自由能函数如何有助于阐明最近观察到的局限于复杂纳米流体几何形状的单个DNA分子的行为？(3)是否有可能提取定量准确的估计熵力的DNA分子拴在一个原子力显微镜（AFM）的悬臂尖与附近的表面相互作用，在最近的AFM实验中尝试？我的研究应该有助于开发这种分析DNA的技术工具。

Polymers are flexible, chain-like molecules that are ubiquitous in nature.  An especially significant polymer of biological relevance is DNA, whose sequence of nucleotides contains the genetic blueprint of an organism. In recent years, there has been intense research activity focused on the development of novel technologies for manipulating and characterizing the physical properties of DNA. Many of these "nanofluidics" technologies involve the transport of DNA into very compact regions of of space. The confinement of polymers in such regions is known to affect their physical properties, an understanding of which is essential for rational design of devices for DNA analysis, as well as for understanding biological phenomena such as chromosome segregation in bacteria. DNA can exist in exotic forms in some organisms. For example, kinetoplasts are structures found in the mitochondria of trypanosome parasites that are composed of thousands of interlocking rings of DNA in two-dimensional "chain-mail" membranes. Recent experiments have characterized some of the unique properties of these objects, which behave like thermalized elastic membranes. Kinetoplasts could serve as an inspiration for the development of novel two-dimensional materials with technological applications.  I will use computer simulation methods to model DNA systems studied in recent experiments. A simulation is a virtual experiment on a model system carried out on a computer. Simulations can be used to interpret the results of experiments and test the validity of theoretical descriptions of experimental systems. The simulations will employ very simple molecular models in order to make the calculations feasible. I will focus on two broad themes. In the first, I will employ 2D networks of interlocking hard rings to model kinetoplasts. I will address the following questions: (1) What is the physical origin of the concave shapes of kinetoplasts? (2) What are the effects of the flexibility of the kinetoplast DNA, the solvent conditions, the presence of perforations, and the linking topology on the average size and shape of the membranes?  The second theme focuses on confinement effects in systems of one or two polymers. I will address the following questions: (1) How does confinement affect the organization and dynamics of two strongly confined polymers under conditions similar to those recently examined in DNA nanofluidics experiments? (2) How can explicitly calculated free-energy functions help elucidate the recently observed behaviour of a single DNA molecule confined to a complex nanofluidic geometry? (3) Is it possible to extract quantitatively accurate estimates of the entropic force for a DNA molecule tethered to an atomic force microscope (AFM) cantilever tip interacting with a nearby surface, as attempted in a recent AFM experiment? My research should help contribute to the development of such technological tools for analyzing DNA.