Mechanical Phase Transitions and Critical Fluctuations in Fiber Networks

人类和动物的大多数软组织，包括皮肤，甚至器官，都依赖于胶原蛋白等坚硬的纤维形成蛋白网络来提供机械支持和稳定性。由另一种叫做纤维蛋白原的纤维蛋白构成的类似网络在伤口愈合中也很重要。这些自然形成的网络的共同之处在于，它们具有内在的机械弹性，当组织在载荷下变形时，它们会变得更加坚硬和稳定。这与合成橡胶或其他高分子材料形成鲜明对比。首席研究员和合作者最近证明，胶原蛋白和其他纤维网络在负载下的自稳定机械反应可以理解为一种相变，有点类似于水在冷却时形成冰的状态变化。然而，纤维网的机械硬化是变形的函数，而不是温度的函数。这个项目的目的是为这种光纤网络的力学发展一个定量的理论模型。胶原蛋白和其他生物聚合物网络的定量和预测理论模型不仅对我们对组织力学的理解很重要，而且有助于合理设计具有类似性质的组织工程合成材料。该项目的一个具体目标也解决了胶原蛋白与透明质酸复合材料抗压性的作用。众所周知，透明质酸在关节的抗压性和润滑中起着重要作用，尽管这种抗压性在先前的光纤网络物理模型中缺失。本项目将培养具有组织工程和材料科学应用前景的化学工程和物理专业研究生。这项研究还将影响莱斯大学化学与生物分子工程、应用物理和材料科学专业本科生和研究生的教学。从全柔性到棒状，半柔性聚合物在许多方面仍然是最具挑战性的理论理解。这种半柔性聚合物在整个生物学中都很重要，从单个细胞内的细胞骨架网络到组织和器官尺度上的细胞外基质。哺乳动物中最普遍的单一蛋白质是胶原蛋白，胶原纤维网络赋予软组织机械稳定性。虽然胶原蛋白和相关的细胞外基质成分已经被广泛研究了几十年，但胶原蛋白和其他纤维网络的理论模型缺乏与经典柔性聚合物理论相媲美的预测能力。这在很大程度上是由于胶原蛋白的几乎完全无热性质，特别是I型胶原蛋白，使得熵弹性等概念不适用。最近的进展是从另一个方向取得的，基于机械相变，如刚性渗透，其中经典的约束计数思想回到麦克斯韦可以用于预测机械稳定性。然而，重要的是，这些想法并不能直接应用于3D光纤网络，因为这种系统远远低于麦克斯韦的等静力稳定性阈值。相反，机械相变的特征是应变的函数，而不是连接的约束，现在已经被PI和细胞外基质力学的合作者从理论上确定并实验证实。然而，这些方面的进展主要是计算性质的，并且仅限于完全的非热状态。该项目旨在(1)为二维和三维非热纤维网络开发预测有效介质理论，(2)扩展该理论和相关计算模型以解决热半柔性聚合物网络问题，(3)研究主动应力在控制半柔性聚合物网络力学中的作用，(4)开发计算模型以解决不可压缩性在细胞外基质力学中的作用。这项研究汇集了统计物理学的思想和方法，从临界现象的流变学研究，可以研究作为应变的函数，而不是温度的实验。这些方法在其他软凝聚态物质和材料科学中具有重要的潜在应用价值。到目前为止，这里要讨论的热方面还没有得到多少关注。这样的效应不仅对更好地理解真实的网络很重要，无论是自然的还是合成的，而且还提高了类似于量子临界系统的新相行为的前景，并增加了在常温下相对容易的实验研究这种效应的前景。纤维网络的定量和预测理论模型不仅对我们对组织力学的理解很重要，而且还有助于合理设计合成材料，例如组织工程。该项目的一部分还旨在解决纤维网络中抗压缩性的作用，这在以前的物理网络模型中很大程度上是缺失的，但对于理解透明质酸和细胞外基质的其他成分的作用是重要的。该项目将支持培养化学工程和物理专业的研究生，并具有在组织工程和材料科学领域的长期应用前景。这项研究还将影响莱斯大学化学与生物分子工程、应用物理和材料科学专业本科生和研究生的教学和课程设置。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。

NONTECHNICAL SUMMARYMost soft tissues including skin and even organs in humans and animals depend on networks of stiff, fiber-forming proteins such as collagen to provide mechanical support and stability. Similar networks, made of another fibrous protein called fibrinogen, are also important in wound healing. Common to these naturally occurring networks is an inherent mechanical resilience in which tissues become more rigid and stable as they are deformed under a load. This is in stark contrast to synthetic rubber or other polymer materials. The principal investigator and collaborators have recently demonstrated that the self-stabilizing mechanical response of collagen and other fiber networks under load can be understood as a phase change, somewhat similar to the change in state of water to form ice on cooling. The mechanical rigidification of fiber networks, however, occurs as a function of deformation rather than temperature. The aim of this project is to develop a quantitative theoretical model for the mechanics of such fiber networks.A quantitative and predictive theoretical model of collagen and other biopolymer networks is not only important for our understanding of tissue mechanics but can also aid in the rational design of synthetic materials with similar properties for tissue engineering. A specific aim of this project also addresses the role of compression resistance in composites of collagen with hyaluronic acid. It is known that hyaluronic acid plays an important role in the compression resistance and lubrication of joints, although such compression resistance has been missing from prior physical models of fiber networks.This project will support the training of graduate students working in Chemical Engineering and Physics, with application perspectives in Tissue Engineering and Materials Science. The research will also impact the teaching of undergraduate and graduate students working in Chemical and Biomolecular Engineering, Applied Physics and Materials Science at Rice University.TECHNICAL SUMMARYOn the spectrum from fully flexible to rod-like, semiflexible polymers remain in many ways the most challenging to understand theoretically. Such semiflexible polymers are important throughout biology, from cytoskeletal networks within individual cells to extracellular matrices at the scale of tissues and organs. The most prevalent single protein in mammals is collagen, and networks of collagen fibers give soft tissues their mechanical stability. Although collagen and related extracellular matrix components have been extensively studied for decades, theoretical models of collagen and other fiber networks with predictive ability comparable to classical flexible polymer theory have been lacking. This is due in large part to the almost entirely athermal nature of especially collagen type I, rendering such concepts as entropic elasticity inapplicable. Recent advances have been made from another direction, based on mechanical phase transitions such as rigidity percolation, where classical constraint counting ideas going back to Maxwell can be useful in predicting mechanical stability. Importantly, however, these ideas do not directly apply to fiber networks in 3D since such systems lie far below Maxwell’s isostatic stability threshold. Instead, signatures of a mechanical phase transition as a function of strain rather than the constraints of connectivity have now been identified theoretically and confirmed experimentally by the PI and collaborators in extracellular matrix mechanics. Advances along these lines have, however, mostly been computational in nature and limited to the fully athermal regime.This project aims to (1) develop a predictive effective medium theory for 2D and 3D athermal fiber networks, (2) extend this and related computational models to address thermal semiflexible polymer networks, (3) study the role of active stresses in controlling semiflexible polymer network mechanics, and (4) develop computational models to address the role of incompressibility in extracellular matrix mechanics.This research brings together statistical physics ideas and approaches from the study of critical phenomena with rheology that can be studied experimentally as a function of strain, rather than temperature. These approaches can have significant potential application to other soft condensed matter and materials science. The thermal aspects to be addressed here have received little attention to date. Not only are such effects important for a better understanding of real networks, natural or synthetic, but these also raise the prospect of novel phase behavior analogous to quantum critical systems, with the added prospect of relative ease of studying such effects experimentally at ordinary temperatures.A quantitative and predictive theoretical model for fiber networks is not only important for our understanding of tissue mechanics but can also aid in the rational design of synthetic materials, e.g., for tissue engineering. Part of this project also aims to address the role of compression resistance in fiber networks, which has largely been missing from prior physical network models but is important for understanding the role of hyaluronic acid and other components of the extracellular matrix.This project will support the training of graduate students working in Chemical Engineering and Physics, with long-term application perspectives in Tissue Engineering and Materials Science. The research will also impact the teaching and curriculum for undergraduate and graduate students working in Chemical and Biomolecular Engineering, Applied Physics and Materials Science at Rice University.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.