Mechanical criticality in extracellular matrices

The mechanics of cells and tissues are largely governed by scaffolds of filamentous proteins that make up the cytoskeleton, as well as extracellular matrices. Evidence is building that such networks, and especially extracellular matrices of collagen exhibit rich mechanical phase behavior. 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. Fiber networks in 3D, however, lie far below this isostatic point, making them naïvely floppy or linearly unstable. We present recent theoretical predictions and experimental evidence for a second-order, critical mechanical phase transition for such systems as a function of strain. We discuss various signatures of transition, including slow stress relaxation and anomalous Poisson ratios, as recently observed in experiments on model tissues. We also develop a field theory for this transition that is not only predictive but also explains the important role of disorder in controlling the non-mean-field aspects of the strain-controlled transition.