Near the onset of rigidity in living and nonliving matter

你是否曾经玩过“捡棍子”游戏，并想知道随机排列的棍子的整个结构如何随着一根棍子的移除而崩溃？你有没有想过皮肤细胞是如何改变形状，爬向伤口愈合的？机械刚性在生物和非生物物质中出现的概念将有助于回答这两个看似不相干的问题。为了探索非生命物质中机械刚性的出现（和破坏），提出的建模将基于一组无摩擦、互斥的软球体；而在生物体内，它会利用一个无序的弹簧网络。PI的团队将通过研究摩擦、颗粒/细丝形状、细丝之间交联的类型、局部机械稳定性等特性来测试这两个模型，这些特性会影响刚性转变的性质。这些模型将用于描述二维和三维系统的机械稳定性，包括颗粒系统、丝状细胞骨架网络和大脑中的生物组织。因此，拟议的工作将材料科学的范围扩展到生命系统，以帮助推动定量生物学的新兴领域。拟议的研究结果将用于开发一种关于生物和非生物系统在本科和研究生阶段的刚性的新课程材料。与锡拉丘兹科学技术博物馆和基督教女青年会的拟议合作将教育公众关于软物质的阴谋。PI将利用她的知识和经验，通过向大四研究生和博士后展示将生物钟和终身教职时钟分离的科学进展，招募女性进入物理科学领域。技术总结：在机械刚度阈值处随机堆积的摩擦颗粒的集合如何随着删除一个接触而不稳定？细胞骨架细丝的集合是如何获得机械刚性来扩展细胞的范围的？在无生命物质中，模型将基于一组无摩擦、互斥的软球体；而在生物体内，它会利用一个无序的弹簧网络。PI的团队将通过研究哪些特性——摩擦、颗粒/细丝形状、细丝之间交联的类型、局部机械稳定性——影响刚性转变的性质，来测试这两个模型的稳健性。为了在非生命系统中测试这种鲁棒性，将使用干扰图的概念研究二维无摩擦、排斥软盘在刚性开始时的机械稳定性的局部特性。有了约束计数、几何和力平衡的信息，PI的团队将开发一个无摩擦颗粒物质中刚度开始的模型。刚性的出现（和破坏）也大量存在于生物物质中。肌动蛋白丝的细胞骨架网络调节其形态以支持细胞结构。提出的研究将通过构建编码更多网络形态（如各向异性和角度约束交联）的无序弹簧网络模型来缩小形态学和力学之间现有的理论差距，以确定哪些方面比其他方面更与刚性的开始相关。此外，将使用与无序弹簧网络相关的顶点模型开发大脑生物组织的定量建模。PI的小组将研究形态学和力学之间的相互作用，以确定神经胶质细胞如何在结构上支持神经元束。拟议的研究结果将用于开发一种关于生物和非生物系统在本科和研究生阶段的刚性的新课程材料。与锡拉丘兹科学技术博物馆和基督教女青年会的拟议合作将教育公众关于软物质的阴谋。PI将通过向高级研究生和博士后展示用于将生物钟和任期时钟分离的科学进展，参与招募女性进入物理科学领域。

NONTECHNICAL SUMMARY Have you ever played a game of "Pick up Sticks" and wondered how an entire structure of randomly arranged sticks can collapse with the removal of just one stick? And have you ever wondered how a skin cell changes shape to crawl towards a wound to heal it? The notion of the onset of mechanical rigidity in both living and nonliving matter will help answer both of these seemingly disparate questions. To explore the emergence (and destruction) of mechanical rigidity in nonliving matter, the proposed modeling will be based on a collection of frictionless, repulsive soft spheres; while in living matter, it will utilize a disordered spring network. The PI's group will test both models by investigating what properties - friction, particle/filament shape, type of crosslinking between filaments, local mechanical stability - affect the nature of the rigidity transition. These models will be used to describe mechanical stability of two- and three-dimensional systems including granular systems, filamentous cytoskeletal networks, and biological tissue in the brain. The proposed work, therefore, extends the reach of materials science to living systems to help drive the emerging field of quantitative biology. The results of the proposed research will be used for development of a new course material on rigidity in both living and nonliving systems at undergraduate and graduate levels. The proposed collaborations with Syracuse Museum of Science and Technology and the YWCA will educate the public about the intrigue of soft matter. The PI will use her knowledge and experience to recruit women to the physical sciences by presenting scientific advances used to decouple the biological clock and the tenure clock to senior graduate students and post-docs. TECHNICAL SUMMARY How does a collection of randomly packed frictional particles at the threshold of mechanical rigidity destabilize with the deletion of just one contact? And how does a collection of cytoskeletal filaments attain mechanical rigidity to extend the reach of a cell? In nonliving matter, the model will be based on a collection of frictionless, repulsive soft spheres; while in living matter, it will utilize a disordered spring network. The PI's group will test the robustness of both models by investigating what properties - friction, particle/filament shape, type of crosslinking between filaments, local mechanical stability - affect the nature of the rigidity transition. To test for this robustness in nonliving systems, the local properties of mechanical stability at the onset of rigidity for frictionless, repulsive soft discs in two dimensions will be studied by using concept of jamming graph. Armed with the information of constraint counting, geometry, and force-balance, the PI's group will develop a model for the onset of rigidity in frictionless, particulate matter. The emergence (and destruction) of rigidity abounds in living matter as well. The actin filament cytoskeletal network adjusts its morphology to support the cell structurally. The proposed research will narrow the existing theoretical gap between morphology and mechanics by building disordered spring network models that encode more of the network morphology, such as anisotropy and angle-constraining crosslinks, to determine which aspects are more relevant to the onset of rigidity than others. Moreover, quantitative modeling of biological tissue in the brain will be developed using vertex models, which are related to disordered spring networks. The PI's group will investigate the interplay between morphology and mechanics to determine how glial cells structurally support bundles of neurons. The results of the proposed research will be used for development of a new course material on rigidity in both living and nonliving systems at undergraduate and graduate levels. The proposed collaborations with Syracuse Museum of Science and Technology and the YWCA will educate the public about the intrigue of soft matter. The PI will be involved in the recruitment of women to the physical sciences by presenting scientific advances used to decouple the biological clock and the tenure clock to senior graduate students and post-docs.