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

聚合物是自然界中普遍存在的柔性链状分子。具有生物相关性的一种特别重要的聚合物是DNA，它的核苷酸序列包含生物体的遗传蓝图。近年来，人们对DNA物理性质的操作和表征的新技术的开发进行了密集的研究活动。其中许多“纳米流体”技术涉及将DNA输送到空间中非常紧凑的区域。众所周知，聚合物在这些区域的限制会影响它们的物理性质，了解这一点对于合理设计DNA分析设备以及理解生物现象(如细菌中的染色体分离)至关重要。DNA可以在某些生物体中以奇异的形式存在。例如，动泡体是在锥虫寄生虫的线粒体中发现的结构，这些结构由数千个互锁的DNA环组成，这些环位于二维的“链状邮件”膜中。最近的实验已经表征了这些物体的一些独特的性质，它们的行为就像热化的弹性膜。运动蛋白可能会对开发具有技术应用的新型二维材料起到启发作用。我将使用计算机模拟方法来对最近实验中研究的DNA系统进行建模。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，并检验实验系统理论描述的有效性。为了使计算可行，模拟将使用非常简单的分子模型。我将集中讨论两个广泛的主题。首先，我将使用互锁硬环的2D网络来模拟运动传播。我将回答以下问题：(1)动泡体凹形的物理来源是什么？(2)动泡体DNA的柔韧性、溶剂条件、穿孔的存在和连接拓扑对膜的平均尺寸和形状的影响是什么？第二个主题集中在一种或两种聚合物体系中的限制效应。我将回答以下问题：(1)在类似于最近在DNA纳米流体实验中检测的条件下，限制如何影响两个强受限聚合物的组织和动力学？(2)显式计算的自由能函数如何有助于阐明最近观察到的受限于复杂纳米流体几何形状的单个DNA分子的行为？(3)是否有可能像最近的AFM实验中所尝试的那样，对拴在原子力显微镜(AFM)悬臂尖端与附近表面相互作用的DNA分子的熵力进行定量准确的估计？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.