Computational modeling of filaments with applications to DNA packing and sedimentation

提案：DMS-0405955 PI：Oscar Gonzalez机构：德克萨斯大学奥斯汀分校题目：细丝的计算建模及其在DNA包装和沉积中的应用研究者将开展两个项目，旨在加深对材料细丝的几何和物理性质的理解。 第一个项目涉及的数值分析的最优包装问题的曲线厚度。 我们的目标是利用全局曲率的概念，开发数值方法优化能量的曲线在三维空间（或框架弯曲，如果扭曲是重要的）受排除体积约束，其中曲线是一个灵活的，固体管的中心线规定的半径。 第二个项目涉及的形状和速度之间的关系，在沉降动力学薄，刚性（或几乎刚性）的细丝。 目的是描述几何特征（例如长度，曲率，管状邻域大小）和拓扑（结型）影响细丝在粘性介质中沉积的可能速度（斯托克斯）对材料细丝如何可以最佳地包装在受限几何形状中以及它们如何可以超螺旋或围绕自身缠绕的理解在大分子（诸如DNA和其他生物大分子）的研究中是非常感兴趣的。化学和生物学中的系统。 虽然最近的建模进展导致了简洁的数学公式，这些问题，研究它们的数值技术得到了相对较少的关注。 第一个研究项目所追求的调查是集中在发展可证明收敛的数值方法研究这些和其他相关的包装问题。 沉降和凝胶电泳是分析DNA和其他聚合物的常用实验室技术。 这些方法利用了这样的观察结果，即当被迫通过粘性流体或通过凝胶时，不同形状的小的、相对刚性的聚合物片段通常以不同的速度行进。 然而，形状和速度之间的一般关系目前还没有很好地理解。 调查员开展的第二个研究项目侧重于确定沉降的形状-速度关系。 从这项研究的结果可能会导致改进的实验室技术，并可能使更多的详细结构信息的聚合物从沉降数据推断。

Proposal: DMS-0405955PI: Oscar GonzalezInstitution: University of Texas at AustinTitle: Computational Modeling of Filaments with Applications to DNA Packing and SedimentationABSTRACTThe investigator will carry out two projects aimed at developing a deeper understanding of the geometrical and physical properties of material filaments. The first project deals with the numerical analysis of optimal packing problems for curves with thickness. The objective is to exploit the concept of global curvature to develop numerical methods for optimizing the energy of a curve in three-dimensional space (or a framed curved if twist is important) subject to an excluded-volume constraint in which the curve is the centerline of a flexible, solid tube of prescribed radius. The second project deals with the relation between shape and speed in the sedimentation dynamics of thin, rigid (or nearly rigid) filaments. The objective is to characterize how features of geometry (such as length, curvature, tubular neighborhood size) and topology (knot type) affect the possible speeds at which a filament can sediment in a viscous (Stokes) fluid.An understanding of how material filaments may be optimally packed in confined geometries and how they may supercoil or wrap around themselves is of great interest in the study of macromolecules such as DNA and other systems in chemistry and biology. While recent modeling advances have led to concise mathematical formulations of such problems, numerical techniques for studying them have received relatively little attention. The first research project pursued by the investigator is focused on the development of provably convergent numerical methods for studying these and other related packing problems. Sedimentation and gel electrophoresis are common laboratory techniques for analyzing DNA and other polymers. These methods exploit the observation that small, relatively stiff polymer fragments of different shape typically travel at different speeds when forced through a viscous fluid or through a gel. However, the general relation between shape and speed is at present not well understood. The second research project pursued by the investigator is focused on the characterization of the shape-speed relation for sedimentation. Results from this research may lead to improved laboratory techniques, and may enable more detailed structural information about polymers to be deduced from sedimentation data.