Rigidity and Shape Transitions in Living and Nonliving Matter

生命和非生命物质的刚性和形状转变

• 批准号: 2204312
• 负责人: Jennifer Schwarz
• 金额: $ 39.2万
• 依托单位: Syracuse University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2204312&HistoricalAwards=false
• 关键词: Rigidity; Shape; Transitions; Living; Nonliving

NONTECHNICAL SUMMARY This award supports theoretical and computational research and education to study materials undergoing transformations from floppy states to rigid states, much like a phase transition from liquid water to ice. Consider a silo of grain initially supporting a person's weight that suddenly collapses beneath them; the grain has transformed from a rigid state to a floppy state. Consider a network of cytoskeletal fibers inside a biological cell becoming less dense to rapidly transform from a rigid state, that provides the cell with mechanical integrity, to a floppy state. These are examples of a rigidity transition. Understanding how rigidity transitions occur in both living and nonliving materials may enable their control - perhaps the grain can be made to keep supporting the person’s weight. Another fundamental property of a material is its shape. Materials can transform from simple to more complex shapes. For example, a developing cerebellum, the “little brain”, begins as a smooth structure and becomes a foliated, or branched, structure in time. A healthy biological cell contains a roughly spherical cell nucleus, while the cell nucleus of a diseased cell may contain bulges and be far from spherical. Abrupt shape transformations may be shape transitions which are prevalent in nature and help determine a system’s functionality. For example, the compartmentalization of DNA in the bulge of a cell nucleus may influence which genes are being transcribed. Understanding shape transitions and shape changes can illuminate how biology works. The PI and her group will explore rigidity and shape transitions in different materials, including biomaterials, to arrive at an overarching, quantitative framework for rigidity and shape. Materials that will be studied include networks of cytoskeletal fibers, grain packings, developing brains, and cell nuclei. The team will investigate connections between properties of loops in the network of cytoskeletal fibers and rigidity. They will construct a theory for the rigidity transition in granular packings that contains rigid clusters and floppy holes to pin down how friction between grains affects the rigidity transition. To study shape transitions, a cellular-based computational model will be developed for predicting how the cerebellum acquires its shape, and to determine how complex shapes arise in brain organoids. A brain organoid is an artificially grown tissue model that mimics key features of a brain and can give insight into its workings. The PI will study a computational and simplified model for the shape and rigidity of a cell nucleus. This project has a component aimed at recruiting more women and marginalized groups into physics. The PI will help lead a new bridge program as well as mentor undergraduates from underrepresented groups during the summer months and address ways to decouple the biological clock and the tenure clock. The PI will also continue to introduce farm physics to school children visiting a u-pick apple orchard/farm in Ithaca, NY. The experience combines physics with orchardry/farming to make physics fun and helps create future physicists. TECHNICAL SUMMARY This award supports theoretical and computational research and education to address open questions regarding emergent rigidity and shape in living and nonliving matter in which disorder is prevalent. The types of materials to be studied include a network of cytoskeletal fibers, granular packings, the developing brain, and a cell nucleus. Such materials toggle between fibrous materials and deformable particulate materials to enable progress towards an overarching, predictive framework for the rigidity and shape of disordered materials. The project is organized into four specific objectives. 1. Rigidity and convexity in underconstrained, disordered fiber networks. Underconstrained, disordered fiber networks can rigidify with sufficient external strain. The PI and her group will explore how geometrical shape attributes of the loops in the network, such as convexity, correlates with rigidity. A focus on convexity may enable direct connections with spin models, which are well-studied, to better understand the nature of the transition. The PI and her group will also determine how the addition of inclusions in the fiber network, which provide additional constraints, influence the emergence of rigidity. They will study the onset of nonlinear rigidity, or compression stiffening/softening, to better understand rigidity as a function of the packing fraction of inclusions, in addition to external strain and spring network connectivity. 2. The universality class search for the frictional jamming transition. The team can readily decompose a two-dimensional, frictional particle packing into rigid clusters interspersed with floppy holes to demonstrate that emergent rigidity, or frictional jamming, is defined as the onset of a spanning rigid cluster. They will now extend the continuum theory for the elasticity of disordered materials further away from the frictional jamming transition to include deformable inclusions to mimic the presence of the floppy holes. Floppy holes, or floppy clusters, arise from the particle mechanics of the packings and are not fixed in size and shape. They grow as the rigidity transition is approached from the rigid phase. The team will formulate a continuum theory for the floppy holes with rules that allow for exchanges between the two cluster types to arrive at a continuum description with two coupled fields. Using this theory, the team aims to investigate the underlying nature of the frictional jamming transition. 3. Developing brain organoids as a shape-changing material. The brain is a living material that changes shape as it develops. Brain organoids also exhibit shape changes as they mature such as containing a core with globular-shaped cells and a boundary layer with extended-shape cells, or cortex. The team will use a 3D vertex model with cells as deformable polyhedrons to study cortex-core formation and cortex-lumen formation. They will also build a cellular-based version of the buckling without bending model for the developing cerebellum. The aim is a predictive model for brain organoid and cerebellar shape at the tissue scale and the cell scale. 4. Activity driven-shape transitions in deformable cell nuclei. The mechanics of a cell nucleus can be minimally modeled as an active polymer(s) representing chromatin confined within, and tethered to, a deformable, thin elastic shell representing a lamina shell. Nuclear blebs are extreme local deformations of the lamina shell. The team will study the initiation of nuclear bleb formation using the minimal mechanical model as a result of external stresses applied to the cell nucleus due to the surrounding cytoplasm and understand how such localized deformations affect chromatin rheology. This avenue of exploration will inspire new types of problems within classical elastic shell theory. These objectives move toward building predictive models for the complex interplay between rigidity and shape that go well beyond mean-field constraint counting and discriminate when shape is synonymous with rigidity and when the shape of one object affects the rigidity of another, as is the case with an active polymer contained within an elastic shell. This project has a component aimed at recruiting more women and marginalized groups into. The PI will help lead a new bridge program as well as mentor undergraduates from underrepresented groups during the summer months and address ways to decouple the biological clock and the tenure clock. The PI will also continue to introduce farm physics to school children visiting a u-pick apple orchard/farm in Ithaca, NY. The experience combines physics with orchardry/farming to make physics fun and helps create future physicists.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

非技术摘要 该奖项支持理论和计算研究和教育，以研究经历从软态到刚性态转变的材料，就像从液态水到冰的相变一样。想象一个最初支撑人体重的谷物筒仓突然在人脚下倒塌；谷物已从刚性状态转变为松软状态。考虑生物细胞内的细胞骨架纤维网络变得密度较低，从而从为细胞提供机械完整性的刚性状态快速转变为松软状态。这些是刚性转变的例子。了解生命和非生命材料中的刚性转变如何发生可能有助于它们的控制——也许可以使谷物继续支撑人的体重。 材料的另一个基本属性是其形状。材料可以从简单的形状转变为更复杂的形状。例如，正在发育的小脑，即“小脑”，一开始是一个光滑的结构，随着时间的推移变成一个叶状或分支结构。 健康的生物细胞含有大致球形的细胞核，而患病细胞的细胞核可能含有凸起且远离球形。 突然的形状转变可能是自然界中普遍存在的形状转变，有助于确定系统的功能。例如，细胞核凸起中 DNA 的区室化可能会影响正在转录的基因。了解形状转变和形状变化可以阐明生物学的工作原理。 PI 和她的团队将探索不同材料（包括生物材料）的刚性和形状转变，以获得刚性和形状的总体定量框架。将研究的材料包括细胞骨架纤维网络、谷物堆积、发育中的大脑和细胞核。该团队将研究细胞骨架纤维网络中环的特性与刚性之间的联系。 他们将构建包含刚性簇和软孔的颗粒填料的刚性转变理论，以确定颗粒之间的摩擦如何影响刚性转变。为了研究形状转变，将开发一种基于细胞的计算模型，用于预测小脑如何获得其形状，并确定大脑类器官如何产生复杂的形状。大脑类器官是一种人工生长的组织模型，可以模仿大脑的关键特征，并可以深入了解其运作方式。 PI 将研究细胞核形状和刚性的计算简化模型。该项目的一个组成部分旨在招募更多女性和边缘群体进入物理学领域。 PI 将帮助领导一个新的桥梁项目，并在夏季指导来自代表性不足群体的本科生，并解决生物钟和终身教职钟脱钩的方法。 PI 还将继续向参观纽约伊萨卡采摘苹果园/农场的学童介绍农场物理学。这种体验将物理学与果园/农业相结合，使物理学变得有趣，并有助于培养未来的物理学家。 技术摘要 该奖项支持理论和计算研究及教育，以解决有关无序现象普遍存在的生物和非生物物质中出现的刚性和形状的开放性问题。要研究的材料类型包括细胞骨架纤维网络、颗粒堆积物、发育中的大脑和细胞核。这种材料在纤维材料和可变形颗粒材料之间切换，以实现无序材料刚性和形状的总体预测框架的进展。该项目分为四个具体目标。 1. 约束不足、无序的光纤网络中的刚性和凸性。受约束不足、无序的光纤网络会因足够的外部应变而变得僵硬。 PI 和她的团队将探索网络中环路的几何形状属性（例如凸度）如何与刚性相关。 对凸性的关注可以使与经过充分研究的自旋模型直接联系起来，以更好地理解转变的本质。 PI 和她的团队还将确定纤维网络中添加的夹杂物（提供额外的约束）如何影响刚性的出现。除了外部应变和弹簧网络连接性之外，他们还将研究非线性刚性或压缩硬化/软化的开始，以更好地理解刚性作为夹杂物堆积分数的函数。 2.摩擦干扰转变的普适性类别搜索。该团队可以轻松地将二维摩擦颗粒堆积分解为散布有软孔的刚性簇，以证明出现的刚性或摩擦干扰被定义为跨越刚性簇的开始。他们现在将扩展无序材料弹性的连续体理论，使其远离摩擦干扰过渡，以包括可变形夹杂物来模拟软盘孔的存在。软孔或软簇是由填料的颗粒力学产生的，并且尺寸和形状不固定。随着从刚性阶段接近刚性转变，它们会增长。该团队将制定软盘孔的连续统理论，其规则允许两种簇类型之间的交换，以达到具有两个耦合场的连续统描述。利用这一理论，该团队旨在研究摩擦干扰转变的根本性质。 3. 开发大脑类器官作为变形材料。大脑是一种有生命的物质，在发育过程中会改变形状。大脑类器官在成熟时也会表现出形状变化，例如包含具有球形细胞的核心和具有扩展形状细胞或皮质的边界层。该团队将使用细胞作为可变形多面体的 3D 顶点模型来研究皮层核心形成和皮层管腔形成。他们还将为发育中的小脑构建基于细胞的屈曲无弯曲模型。 目的是在组织尺度和细胞尺度上建立脑类器官和小脑形状的预测模型。 4.可变形细胞核中的活动驱动形状转变。细胞核的力学可以最低限度地建模为代表染色质的活性聚合物，该聚合物被限制在并束缚在代表层壳的可变形薄弹性壳内。核泡是层壳的极端局部变形。该团队将使用最小机械模型研究由于周围细胞质而对细胞核施加外部应力导致核泡形成的启动，并了解这种局部变形如何影响染色质流变学。这种探索途径将激发经典弹性壳理论中的新型问题。 这些目标旨在为刚性和形状之间复杂的相互作用建立预测模型，该模型远远超出了平均场约束计数，并且能够区分何时形状与刚性同义以及何时一个物体的形状影响另一个物体的刚性，就像弹性壳中包含的活性聚合物的情况一样。 该项目的一个组成部分旨在招募更多妇女和边缘化群体加入。 PI 将帮助领导一个新的桥梁项目，并在夏季指导来自代表性不足群体的本科生，并解决生物钟和终身教职钟脱钩的方法。 PI 还将继续向参观纽约伊萨卡采摘苹果园/农场的学童介绍农场物理学。这种体验将物理学与果园/农业相结合，使物理学变得有趣，并帮助培养未来的物理学家。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。