Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of connections between nodes exceeds the isostatic threshold are networks stable [1]. Upon increasing the connectivity through this point, such networks undergo a mechanical phase transition from a floppy to a rigid phase. However, even subisostatic networks become rigid when subjected to sufficiently large deformations. To study this strain-controlled transition, we perform a combination of computational modeling of fibre networks and experiments on networks of type I collagen fibers, which are crucial for the integrity of biological tissues. We show theoretically that the development of rigidity is characterized by a strain-controlled continuous phase transition with signatures of criticality. Our experiments demonstrate mechanical properties consistent with our model, including the predicted critical exponents. We show that the nonlinear mechanics of collagen networks can be quantitatively captured by the predictions of scaling theory for the straincontrolled critical behavior over a wide range of network concentrations and strains up to failure of the material.As shown by Maxwell, networks with only central-force interactions exhibit a transition from a floppy to rigid phase at the isostatic point, where the local coordination number, or connectivity z equals the threshold value of z = 2d in d dimensions [1]. At this point, the number of degrees of freedom is just balanced by the number of constraints, and the system is marginally stable to small deformations. The jamming transition [2][3][4][5][6] in granular materials and rigidity percolation [7][8][9][10] in disordered spring networks are examples of such a transition. An important feature of these systems is the order of the transition. Jamming exhibits signatures of both first-and second-order transitions, with discontinuous behaviour of the bulk modulus and continuous variation of the shear modulus [5,11,12]. For networks of springs or fibres, the transition from floppy to rigid is a continuous phase transition, in both bulk and shear moduli [2, 5, 7, 7, 8,14].Interestingly, the structural networks in biology almost always have connectivities below the central-force iso- static point. Networks such as the extracellular matrices of collagen that make up tissue are strictly sub-isostatic with respect to central forces: their typical connectivity is between 3 (local branching) and 4 (binary crosslinking), placing them below both 2D and 3D isostatic thresholds [17,18]. Such sub-isostatic networks can, nevertheless, become rigid as a result of other mechanical constraints, such as fibre bending [4, 7,19], or when subjected to external strain [21]. The threshold strain, at which the transition occurs, depends on the nature of applied deformation (shear or tensile) and on the average connectivity of the network, in particular, and othe...

The ability of cells to sense and respond to mechanical signals is vital in development and healthy tissue functioning. Many diseases are related to either changing mechanical properties of the tissue, or changes in the ability of cells to sense mechanical signals. This sensing occurs, in part, at integrin-associated complexes (IACs) that form sites of attachment between the cell and the extracellular matrix (ECM). In this review, we discuss the complex mechanical signals of the ECM. We will also outline how IACs are involved in cellular sensing of these mechanical properties, focussing on the molecular mechanisms of key adhesion molecules. Finally, the cellular mechanisms of mechanotransduction considering mechanosensing and signalling aspects of the core proteins in FAs are discussed and open questions outlined.

Cells actively sense and process mechanical information that is provided by the extracellular environment to make decisions about growth, motility and differentiation. It is important to understand the underlying mechanisms given that deregulation of the mechanical properties of the extracellular matrix (ECM) is implicated in various diseases, such as cancer and fibrosis. Moreover, matrix mechanics can be exploited to program stem cell differentiation for organ-on-chip and regenerative medicine applications. Mechanobiology is an emerging multidisciplinary field that encompasses cell and developmental biology, bioengineering and biophysics. Here we provide an introductory overview of the key players important to cellular mechanobiology, taking a biophysical perspective and focusing on a comparison between flat versus three dimensional substrates. This article is part of a Special Issue entitled: Mechanobiology.

Collagen forms fibrous networks that reinforce tissues and provide an extracellular matrix for cells. These networks exhibit remarkable strain-stiffening properties that tailor the mechanical functions of tissues and regulate cell behavior. Recent models explain this nonlinear behavior as an intrinsic feature of disordered networks of stiff fibers. Here, we experimentally validate this theoretical framework by measuring the elastic properties of collagen networks over a wide range of self-assembly conditions. We show that the model allows us to quantitatively relate both the linear and nonlinear elastic behavior of collagen networks to their underlying architecture. Specifically, we identify the local coordination number (or connectivity) 〈z〉 as a key architectural parameter that governs the elastic response of collagen. The network elastic response reveals that 〈z〉 decreases from 3.5 to 3 as the polymerization temperature is raised from 26 to 37°C while being weakly dependent on concentration. We furthermore infer a Young's modulus of 1.1 MPa for the collagen fibrils from the linear modulus. Scanning electron microscopy confirms that 〈z〉 is between three and four but is unable to detect the subtle changes in 〈z〉 with polymerization conditions that rheology is sensitive to. Finally, we show that, consistent with the model, the initial stress-stiffening response of collagen networks is controlled by the negative normal stress that builds up under shear. Our work provides a predictive framework to facilitate future studies of the regulatory effect of extracellular matrix molecules on collagen mechanics. Moreover, our findings can aid mechanobiological studies of wound healing, fibrosis, and cancer metastasis, which require collagen matrices with tunable mechanical properties.