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.

该奖项支持理论和计算研究和教育，以研究从软盘状态到刚性状态的转变，就像从液态水到冰的相变一样。想想一个谷仓，最初支撑着一个人的体重，突然在他们下面倒塌；谷物已经从刚性状态转变为软性状态。考虑一个生物细胞内的细胞骨架纤维网络变得不那么密集，从而迅速从提供细胞机械完整性的刚性状态转变为软性状态。这些都是刚性转变的例子。了解生物和非生物材料的刚性转变是如何发生的，可以使它们得到控制——也许可以使谷物保持支撑人的体重。材料的另一个基本特性是它的形状。材料可以从简单的形状转变为更复杂的形状。例如，一个发育中的小脑，即“小脑”，开始时是一个光滑的结构，后来变成了一个叶状或分枝的结构。一个健康的生物细胞含有一个大致为球形的细胞核，而一个患病细胞的细胞核可能含有凸起并且远离球形。突发性形状转换可能是自然界中普遍存在的形状转换，有助于确定系统的功能。例如，细胞核凸起处DNA的区隔化可能会影响哪些基因正在转录。了解形状转换和形状变化可以阐明生物学是如何工作的。PI和她的团队将探索不同材料（包括生物材料）的刚性和形状转换，以达到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、谷物包装、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。为了研究形状转换，将开发一种基于细胞的计算模型来预测小脑如何获得其形状，并确定复杂形状如何在脑类器官中出现。脑类器官是一种人工培养的组织模型，可以模仿大脑的关键特征，并能深入了解其工作原理。PI将研究细胞核形状和刚性的计算和简化模型。这个项目有一个组成部分，旨在招募更多的妇女和边缘群体进入物理学。在夏季的几个月里，PI将帮助领导一个新的桥梁项目，并指导来自代表性不足群体的本科生，并寻求将生物钟和终身教职时钟脱钩的方法。PI还将继续向参观纽约州伊萨卡市u-pick苹果园/农场的学生介绍农场物理。这种体验将物理与果园/农场结合起来，使物理变得有趣，并有助于培养未来的物理学家。该奖项支持理论和计算研究和教育，以解决有关无序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、颗粒填料、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，使无序材料的刚性和形状朝着一个总体的、可预测的框架发展。该项目分为四个具体目标。1. 欠约束无序光纤网络中的刚性和凸性。欠约束、无序的光纤网络可以在足够的外部应变下发生刚性。PI和她的团队将探索网络中环路的几何形状属性（如凸性）如何与刚性相关。对凹凸性的关注可能会使自旋模型（已经得到了很好的研究）直接联系起来，从而更好地理解跃迁的本质。PI和她的团队还将确定光纤网络中添加的内含物（提供额外的约束）如何影响刚性的出现。他们将研究非线性刚度的开始，或压缩硬化/软化，以更好地理解刚度作为夹杂物填料分数的函数，以及外部应变和弹簧网络连接。2. 通用性类搜索摩擦干扰过渡。该团队可以很容易地将二维摩擦颗粒填料分解成带有软孔的刚性簇，以证明突发性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统理论，使其远离摩擦干扰过渡，包括可变形的内含物来模拟软孔的存在。软孔或软簇是由填料的颗粒力学产生的，其大小和形状并不固定。它们随着从刚性相向刚性转变而增长。该团队将为软孔制定一个连续统理论，该理论的规则允许两种簇类型之间的交换，从而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过渡的潜在性质。3. 开发大脑类器官作为一种可变形的材料。大脑是一种有生命的物质，它会随着发育而改变形状。脑类器官在成熟的过程中也表现出形状的变化，比如包含一个由球状细胞组成的核心和一个由延伸形状细胞组成的边界层，即大脑皮层。该团队将使用一个三维顶点模型，将细胞作为可变形多面体来研究皮质-核心形成和皮质-腔体形成。他们还将为发育中的小脑建立一个基于细胞的无弯曲屈曲模型。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. 可变形细胞核中活动驱动的形状转变。细胞核的力学可以最小限度地建模为一个活性聚合物，代表染色质被限制在一个可变形的薄弹性壳中，并与之相连，代表层状壳。核泡是板壳的极端局部变形。该团队将使用最小力学模型研究核泡形成的起始，这是由于周围细胞质施加于细胞核的外部应力造成的，并了解这种局部变形如何影响染色质流变。这一探索途径将激发经典弹性壳理论中的新类型问题。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，这些模型远远超出了平均场约束计数，并区分形状何时与刚性同义，以及一个物体的形状何时影响另一个物体的刚性，就像弹性外壳中含有活性聚合物的情况一样。这个项目有一个组成部分，旨在招募更多的妇女和边缘群体。在夏季的几个月里，PI将帮助领导一个新的桥梁项目，并指导来自代表性不足群体的本科生，并寻求将生物钟和终身教职时钟脱钩的方法。PI还将继续向参观纽约州伊萨卡市u-pick苹果园/农场的学生介绍农场物理。这种体验将物理与果园/农场结合起来，使物理变得有趣，并有助于培养未来的物理学家。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。