CAREER: The Statistical Mechanics of Filamentous Assemblies

技术总结这个职业奖项支持理论和计算研究，以及有关纳米级细丝的超分子组装的教育。由于生物纤维本身的灵活性和它们之间相互作用的复杂性，生物纤维给理论研究带来了固有的挑战。这些效应是由长波物理控制的，既代表了沿细丝的软变形，也代表了细丝间堆积几何形状的集体效应。PI将研究源于生物细丝的共同结构的丝状组件的统计和热力学性质。也就是说，生物纤维普遍是长的、灵活的和螺旋状的。这项研究的目的有三：1)建立手性诱导的拓扑缺陷在有限直径纤维束形成中的作用；2)建立蛋白质介导的丝状肌动蛋白集束的统计理论；3)探索纯净和非均匀细丝集合体结晶的统计机制。项目(1)：PI将建立密集生物纤丝束背景下二维和手性有序材料之间几何受挫的基本结果。PI将专注于屏蔽远程应力的倾斜度所起的作用，这些应力本身是由相邻细丝之间的手性相互作用引起的。该PI旨在阐明手性对分子组装的影响，并提供对生物细丝组装机制的洞察，这些组装机制天生就受到尺寸的限制。项目(2)：PI旨在构建一个统计力学框架，一个耦合的晶格-气体和晶格自旋模型，以探索平行肌动蛋白束的组装热力学。我们的目标是确定f-肌动蛋白和束组件各自的螺旋和六重对称性之间的内在挫折如何引起交联蛋白的协同结合，并影响束的形成。项目(3)：PI将研究丝状系统在经历从二维液晶到真正的三维固体的异常复杂的相变时的临界性质。PI进一步旨在评估多分散长丝结晶所固有的淬火杂质的作用，并扩大我们对软材料中无序作用的知识。教育部分支持开发一项新的教育计划，该计划利用现有的中心和教师资源，为本科生创建软物质理论研究暑期计划。该计划旨在提高学生的技能，使他们能够参与正在进行的理论研究项目。这个项目向学生介绍软材料建模的方法和挑战，以及这一领域研究的兴奋。非技术总结这个职业奖项支持理论和计算研究，以及关于尺寸为纳米级的大分子组成的细丝组装的教育。十亿分之一米。像这样的丝状集合体存在于生物细胞内，并在赋予它们结构完整性方面发挥着重要作用。该奖项支持研究，以了解丝状集合体如何将自己组织成更复杂的结构。这对丝状组件的结构和机械性能有重要影响。这项研究的各个方面将与使用x射线研究细胞中的丝束的实验工作合作进行。PI试图揭示也将适用于纳米级结构的新合成材料设计的基本原理。这项研究是数学和物理科学与生物学之间的基础研究的一个例子，这有可能促进两者的发展。教育部分支持一项新的教育计划，该计划利用现有的中心和教师资源，为本科生创建软物质理论研究暑期计划。该计划旨在提高学生的技能，使他们能够参与正在进行的理论研究项目。本课程向学生介绍软材料建模的方法和挑战，以及这一领域研究的兴奋。

TECHNICAL SUMMARYThis CAREER award supports theoretical and computational research, and education on supermolecular assemblies of nanoscale filaments. Biofilaments present inherent challenges to theoretical study owing to the flexibility of the filaments themselves and the complexity of interactions among them. These effects are governed by long-wavelength physics, representing both soft deformations along filaments, as well as collective effects of inter-filament packing geometry.The PI will investigate the statistical and thermodynamic properties of filamentous assemblies that derive from the common structure of biological filaments. Namely, biofilaments are universally long, flexible and helical. The research addresses three aims: 1) establish the role of chirally-induced topological defects in finite-diameter bundle formation; 2) build a statistical theory of protein-mediated bundling of filamentous actin; and 3) explore the statistical mechanics of crystallization of pure and inhomogeneous filament assemblies.Project (1): The PI will establish a fundamental consequence of the geometric frustration between two dimensional and chirally ordered materials in the context of dense biofilament bundles. The PI will focus on the role played by disclinations that screen long-range stresses, which are themselves induced by chiral interactions between neighboring filaments. The PI aims to illuminate the influence of chirality on molecular assembly and provide insight into assembly mechanisms of biological filaments that are inherently limited in size. Project (2): The PI aims to construct a statistical mechanical framework, a coupled lattice-gas and lattice spin model, to explore the assembly thermodynamics of parallel actin bundles. The goal is to determine how an intrinsic frustration between the respective helical and six-fold symmetries of f-actin and bundle assemblies gives rise to cooperative binding of cross-linking proteins and influences bundle formation. Project (3): The PI will investigate the critical properties of filamentous systems as they pass through an unusually complex phase transition from two dimensional liquid-crystals to true three dimensional solids. The PI further aims to assess the role of quenched impurities inherent to crystallization of polydisperse filaments and expand our knowledge of the role of disorder in soft materials.The education component supports an effort to develop a new educational program that leverages existing center and faculty resources to create a Soft Matter Research in Theory summer program for undergraduate students. The program is designed to enhance the skills of students and enable them to participate in ongoing theoretical research projects. This program introduces students to the methods and challenges of modeling soft materials and the excitement of research in this area.NONTECHNICAL SUMMARYThis CAREER award supports theoretical and computational research, and education on assemblies of filaments composed of large molecules that have dimensions on scale of a nanometer ? a billionth of a meter. Filamentous assemblies like these are found inside biological cells and play an important role in giving them structural integrity. This award supports research to understand how filamentous assemblies organize themselves into more complex structures. This has important consequences for the structural and mechanical properties of filamentous assemblies. Aspects of the research will be done in collaboration with experimental efforts that use x-rays to study filament bundling in cells. The PI seeks to uncover fundamental principles that will also apply to the design of new synthetic materials that are structured on the nanometer scale.This research is an example of fundamental research in the mathematical and physical sciences at the boundaries with biology which has the potential to advance both.The education component supports an effort to develop a new educational program that leverages existing center and faculty resources to create a Soft Matter Research in Theory summer program for undergraduate students. The program is designed to enhance the skills of students and enable them to participate in ongoing theoretical research projects. This program introduces students to the methods and challenges of modeling soft materials and the excitement of research in this area.