Mechanical Phase Transitions and Critical Fluctuations in Fiber Networks

William Marsh Rice University, Houston TX

Investigators

Abstract

NONTECHNICAL SUMMARY Most 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 SUMMARY On 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.