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刚性纤维形成蛋白质的网络来提供机械支撑和稳定性。类似的网络，由另一种纤维蛋白质纤维蛋白原组成，在伤口愈合中也很重要。这些天然存在的网络的共同点是固有的机械弹性，其中组织在负载下变形时变得更加刚性和稳定。这与合成橡胶或其他聚合物材料形成鲜明对比。主要研究者和合作者最近证明，胶原蛋白和其他纤维网络在负载下的自稳定机械响应可以理解为相变，有点类似于水在冷却时形成冰的状态变化。然而，纤维网络的机械硬化是作为变形而不是温度的函数发生的。本项目的目的是建立一个定量的理论模型来描述这种纤维网络的力学行为。胶原蛋白和其他生物聚合物网络的定量和预测性理论模型不仅对我们理解组织力学很重要，而且可以帮助我们合理设计具有相似性能的组织工程合成材料。该项目的一个具体目标还涉及抗压性在胶原蛋白与透明质酸复合材料中的作用。透明质酸在关节的抗压性和润滑性方面发挥着重要作用，但在以往的纤维网物理模型中，这种抗压性是缺失的。本项目将支持培养化学工程和物理学专业的研究生，在组织工程和材料科学方面具有应用前景。这项研究还将影响莱斯大学化学和生物分子工程、应用物理和材料科学专业的本科生和研究生的教学。技术总结在从完全柔性到棒状的范围内，半柔性聚合物在许多方面仍然是理论上最具挑战性的。这种半柔性聚合物在整个生物学中是重要的，从单个细胞内的细胞骨架网络到组织和器官规模的细胞外基质。哺乳动物中最普遍的单一蛋白质是胶原蛋白，胶原纤维的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被广泛研究了几十年，胶原蛋白和其他纤维网络的预测能力与经典的柔性聚合物理论的理论模型一直缺乏。这在很大程度上是由于尤其是I型胶原的几乎完全无热的性质，使得诸如熵弹性的概念不适用。最近的进展已经从另一个方向，基于机械相变，如刚性渗透，其中经典的约束计数的想法可以追溯到麦克斯韦可以是有用的预测机械稳定性。然而，重要的是，这些想法并不直接应用于3D中的光纤网络，因为这样的系统远低于麦克斯韦的均衡稳定性阈值。相反，作为应变的函数而不是连接性的约束的机械相变的签名现在已经在理论上被确定，并由PI和合作者在细胞外基质力学实验证实。然而，这方面的进展大多是计算性的，仅限于完全无热状态。该项目旨在（1）开发二维和三维无热纤维网络的预测有效介质理论，（2）扩展该模型和相关计算模型以解决热问题。半柔性聚合物网络，（3）研究主动应力在控制半柔性聚合物网络力学中的作用，和（4）开发计算模型来解决不可压缩性在细胞外基质力学中的作用。这项研究将统计物理学的思想和方法从研究临界现象与流变学结合起来，流变学可以作为应变而不是温度的函数进行实验研究。这些方法对其他软凝聚态物质和材料科学具有重要的潜在应用价值。 到目前为止，这里要解决的热方面很少受到关注。这些效应不仅对更好地理解自然或合成的真实的网络很重要，而且还提高了类似于量子临界系统的新相行为的前景，一个定量的和预测性的纤维网络理论模型不仅对我们理解组织力学很重要，而且还可以帮助我们理解组织力学，合成材料的合理设计，例如，用于组织工程。本项目的一部分还旨在解决纤维网络中的抗压性的作用，这在以前的物理网络模型中基本上是缺失的，但对于理解透明质酸和细胞外基质的其他成分的作用很重要。本项目将支持培养化学工程和物理学研究生，长期应用于组织工程和材料科学。该研究还将影响莱斯大学化学和生物分子工程、应用物理和材料科学专业的本科生和研究生的教学和课程。该奖项反映了NSF的法定使命，并通过使用基金会的智力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.