Mechanical Phase Transitions and Critical Fluctuations in Fiber Networks

非技术性总结人类和动物的大多数软组织，包括皮肤甚至器官，都依赖于胶原等僵硬的纤维形成蛋白网络来提供机械支持和稳定性。类似的网络由另一种名为纤维蛋白原的纤维蛋白组成，在伤口愈合中也很重要。这些自然形成的网络的共同之处是固有的机械弹性，在这种情况下，组织在负荷下变形时变得更加坚硬和稳定。这与合成橡胶或其他聚合物材料形成了鲜明的对比。主要研究人员和合作者最近证明，胶原和其他纤维网络在负荷下的自稳定力学反应可以理解为相变，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变形而不是温度的函数。本项目的目的是建立一种定量的纤维网络力学理论模型。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理解组织力学具有重要意义，而且有助于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与透明质酸复合材料中的作用。众所周知，透明质酸在关节的抗压和润滑中起着重要的作用，尽管这种抗压作用在以前的纤维网络物理模型中是缺失的。该项目将支持在组织工程和材料科学中具有应用前景的化学工程和物理专业的研究生培养。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。技术总结在从全柔性到棒状的光谱中，半柔性聚合物在许多方面仍然是理论上最难理解的。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，胶原蛋白纤维网络使软组织具有机械稳定性。尽管胶原和相关的细胞外基质成分已经被广泛研究了几十年，但胶原和其他纤维网络的理论模型一直缺乏可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I型胶原几乎完全无热的性质，使得熵弹性等概念不适用。最近从另一个方向取得了进展，基于机械相变，如刚性渗流，其中回到麦克斯韦的经典约束计数思想在预测机械稳定性方面是有用的。然而，重要的是，这些想法并不直接适用于3D光纤网络，因为这样的系统远远低于麦克斯韦的均衡稳定阈值。相反，作为应变的函数而不是连接性的限制的机械相变的特征现在已经被PI和细胞外基质力学的合作者从理论上和实验上证实。然而，这些方面的进展大多是计算的，仅限于完全无热状态。本项目旨在(1)开发2D和3D无热光纤网络的预测有效介质理论，(2)扩展该理论和相关计算模型以处理热半柔性聚合物网络，(3)研究主动应力在控制半柔性聚合物网络力学中的作用，以及(4)开发计算模型以解决不可压缩在细胞外基质力学中的作用。这项研究汇集了从流变学的临界现象研究的统计物理思想和方法，可以通过实验研究作为应变的函数，而不是温度。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，这里要讨论的热方面几乎没有受到关注。这些效应不仅对更好地理解真实的网络非常重要，无论是自然的还是合成的，而且这些效应也带来了类似于量子临界系统的新的相行为的前景，以及在常温下相对容易地通过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于我们对组织力学的理解很重要，而且还可以帮助合成材料的合理设计，例如用于组织工程。这个项目的一部分还旨在解决纤维网络中压缩阻力的作用，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是重要的。这个项目将支持在化学工程和物理工作的研究生的培训，并在组织工程和材料科学方面具有长期的应用前景。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优势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.