Near the onset of rigidity in living and nonliving matter

非技术摘要你有没有玩过“捡起棍子”的游戏，想知道只拿掉一根棍子，整个随机排列的棍子结构怎么就会坍塌？你有没有想过皮肤细胞是如何改变形状来爬向伤口来治愈它的？有生命和无生命物质的机械刚性的概念将有助于回答这两个看似不同的问题。为了探索非生物中机械刚性的出现(和破坏)，建议的建模将基于一组无摩擦、相斥的软球；而在生物中，它将利用无序的弹簧网络。PI的研究小组将通过调查哪些特性--摩擦、颗粒/细丝形状、细丝之间的交联类型、局部机械稳定性--影响刚性转变的性质，来测试这两个模型。这些模型将被用来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，这项拟议的工作将材料科学的范围扩展到生命系统，以帮助推动新兴的数量生物学领域。拟议的研究结果将用于编写关于本科生和研究生水平的生物和非生物系统中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拟议的合作将教育公众了解软物质的奥秘。PI将利用她的知识和经验，通过向高级研究生和博士后介绍用于将生物时钟和终身教职时钟脱钩的科学进步，来招募女性进入物理学。技术概述一组随机堆积的摩擦颗粒在机械刚性门槛处如何在仅删除一个触点的情况下不稳定？一组细胞骨架细丝如何达到机械刚性以延长细胞的伸展范围？在非生物物质中，该模型将基于一组无摩擦的、相互排斥的软球；而在生物物质中，它将利用一个无序的弹簧网络。PI的小组将通过调查哪些属性-摩擦、颗粒/细丝形状、细丝之间的交联类型、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。为了在非生物系统中测试这种稳健性，将使用干扰图的概念来研究无摩擦、排斥的二维软盘在刚性开始时的机械稳定性的局部特性。利用约束计数、几何学和力平衡的信息，PI的小组将开发一个无摩擦颗粒物质中刚性开始的模型。刚性的出现(和破坏)在生物中也比比皆是。肌动蛋白细丝细胞骨架网络调整其形态以支持细胞的结构。这项拟议的研究将通过建立无序的弹簧网络模型来缩小形态和力学之间的现有理论差距，该模型编码了更多的网络形态，如各向异性和角度约束的交联键，以确定哪些方面比其他方面与刚性的开始更相关。此外，将使用与无序的弹簧网络相关的顶点模型来开发大脑中生物组织的定量建模。PI的研究小组将研究形态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编写关于本科生和研究生水平的生物和非生物系统中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拟议的合作将教育公众了解软物质的奥秘。国际和平研究所将通过向高级研究生和博士后介绍用于将生物时钟与终身教职时钟脱钩的科学进展，参与招募妇女进入自然科学。

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.