The mechanics of cells and tissues are largely governed by scaffolds of filamentous proteins that make up the cytoskeleton, as well as extracellular matrices. The observed rheology of these systems is particularly rich in their nonlinear response. The constituent biopolymers are typically much more rigid to bending than synthetic polymers, which tends to make the rheology of biopolymer networks more challenging and subtle to understand. As we argue, the rheology of stiff polymer networks can be partly understood in terms of mechanical phase transitions, especially in the limit of highly rigid, athermal fibers. A classic example of a mechanical phase transition was identified by Maxwell for macroscopic engineering structures: networks of struts or springs exhibit a continuous, second-order phase transition at the isostatic point, where the number of constraints imposed by connectivity just equals the number of mechanical degrees of freedom. We will present recent theoretical predictions and experimental evidence for mechanical phase transitions and critical phenomena in biopolymer networks. We demonstrate quantitative agreement between predicted nonlinear rheology and the measured elastic response of collagen networks. We also show how critical fluctuations associated with a mechanical phase transition can lead to strong anomalies in the normal stress of such systems.
Fred MacKintosh received his PhD in Theoretical Physics from Princeton University. Following a postdoc at Exxon Corporate Research, he joined the Physics Department at the University of Michigan as Assistant, then Associate Professor. In 2001, Fred joined the Vrije Universiteit in Amsterdam as Professor of Theoretical Physics of Complex Systems. Since 2016, he has been the Abercrombie Professor of Chemical and Biomolecular Engineering at Rice University, as well as a member of the Center for Theoretical Biological Physics, with additional appointments in the Departments of Chemistry and Physics and Astronomy. His primary research interests include the physics of biopolymers and their networks, cell mechanics and non-equilibrium aspects of active and living soft matter.