Isostatic Elasticity in a Biomolecular Network

该研究计划将研究柔软，网络化材料的机械性能如何从纳米级结构和它们的结和股的刚度中产生。 柔软的网络材料在生物学和技术中无处不在;例子包括活细胞的细胞骨架，弹性体和水凝胶。从历史上看，解释这些材料机械性能的主要模型是弹性橡胶模型。该模型将网络股视为熵弹簧，并预测材料的刚度仅取决于股浓度和温度-值得注意的是，它没有考虑网络结构的任何其他方面。 然而，经典力学告诉我们，宏观网络的刚度受到网络价（从节点发出的梁的数量）的强烈影响。这种观点由麦克斯韦正式化，被称为均衡准则：由销连接的刚性梁的网络，梁在销连接处自由旋转，必须具有6或更高的化合价才是刚性的，而较低化合价的网络是松弛的。通过研究（独立于化合价的）橡胶弹性和（依赖于化合价的）等静压如何相互作用以产生柔软的网络材料的关键机械特性，如变形性和失效，这项工作将产生一个精确的数据集，这将促进等静压变形和失效本构模型的发展，从而能够在工程背景下合理预测材料行为。 这项研究充满了强烈的教育成分：研究项目将提供给本科生暑期实习，研究成果将融入课堂教学。这些活动，沿着与研究生的参与，确保该项目将大大有助于培养下一代的研究人员在这个不断增长的领域。研究的具体目标是发现结价，旋转自由度和链刚度决定线性和非线性网络力学的关系。这将通过对自组装DNA颗粒形成的纳米级定义的网络材料的流变学测量进行实验。 DNA的使用提供（i）由于DNA的半刚性结构而减小的熵效应;（ii）通过DNA杂交对接头和链结构的设计控制;以及（iii）通过改变DNA杂交的局部稳定性的光可切换部分对其进行动态控制。该项目将推进机械工程和材料科学交叉领域的知识基础，并展示对网络材料极端机械性能的前所未有的访问和控制。该奖项反映了NSF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。

This research program will investigate how the mechanical properties of soft, networked materials arise from the nanoscale structure and stiffness of their junctions and strands. Soft, networked materials are ubiquitous in biology and technology; examples include the cytoskeleton of living cells, elastomers, and hydrogels. Historically, the dominant model for explaining these materials' mechanical properties was the rubber model of elasticity. This model views network strands as entropic springs and predicts that the material's stiffness depends only on strand concentration and temperature—notably, it does not take any other aspect of network structure into account. However, classical mechanics tells us that the rigidity of a macroscopic network is strongly affected by the network's valence (the number of beams emanating from a joint). This insight, formalized by Maxwell, is known as the isostatic criterion: Networks of rigid beams connected by pin joints, at which beams freely rotate, must have a valence of 6 or more to be rigid, while networks of lower valence are floppy. By investigating how (valence-independent) rubber elasticity and (valence-dependent) isostaticity interact to create a soft, networked material's key mechanical properties, like deformability and failure, this work will produce a precision data set that will catalyze the development of constitutive models of isostatic deformation and failure, thus enabling rational prediction of material behavior in an engineering context. This research is imbued with a strong educational component: research projects will be offered to undergraduates for summer internships and research results will be integrated into classroom teaching. These activities, along with the involvement of graduate students, ensure that the project will significantly contribute to training the next generation of researchers in this growing field.The specific goal of the research is to discover the relationship by which junction valence, rotational freedom, and strand stiffness determine both linear and non-linear network mechanics. This will be pursued experimentally by rheological measurements of nanoscopically-defined networked materials formed from self-assembled DNA particles. The use of DNA offers (i) diminished entropic effects due to DNA’s semi-rigid structure; (ii) design control over joint and strand structure via DNA hybridization; and, (iii) dynamic control of the same via light-switchable moieties that alter the local stability of DNA hybridization. This project will advance the knowledge base at the intersection of mechanical engineering and material science and demonstrate unprecedented access to and control over the extreme mechanical properties enabled in networked materials.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.