skip to main content

Title: Modulus of Fibrous Collagen at the Length Scale of a Cell
The extracellular matrix provides macroscale structural support to tissues as well as microscale mechanical cues, like stiffness, to the resident cells. As those cues modulate gene expression, proliferation, differentiation, and motility, quantifying the stiffness that cells sense is crucial to understanding cell behavior. Whereas the macroscopic modulus of a collagen network can be measured in uniform extension or shear, quantifying the local stiffness sensed by a cell remains a challenge due to the inhomogeneous and nonlinear nature of the fiber network at the scale of the cell. To address this challenge, we designed an experimental method to measure the modulus of a network of collagen fibers at this scale. We used spherical particles of an active hydrogel (poly N-isopropylacrylamide) that contract when heated, thereby applying local forces to the collagen matrix and mimicking the contractile forces of a cell. After measuring the particles’ bulk modulus and contraction in networks of collagen fibers, we applied a nonlinear model for fibrous materials to compute the modulus of the local region surrounding each particle. We found the modulus at this length scale to be highly heterogeneous, with modulus varying by a factor of 3. In addition, at different values of applied strain, we observed both strain stiffening and strain softening, indicating nonlinearity of the collagen network. Thus, this experimental method quantifies local mechanical properties in a fibrous network at the scale of a cell, while also accounting for inherent nonlinearity.  more » « less
Award ID(s):
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Experimental Mechanics
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    Cells sense mechanical signals within the extracellular matrix, the most familiar being stiffness, but matrix stiffness cannot be simply described by a single value. Randomness in matrix structure causes stiffness at the scale of a cell to vary by more than an order of magnitude. Additionally, the extracellular matrix contains ducts, blood vessels, and, in cancer or fibrosis, regions with abnormally high stiffness. These different features could alter the stiffness sensed by a cell, but it is unclear whether the change in stiffness is large enough to overcome the noise caused by heterogeneity due to the random fibrous structure. Here we used a combination of experiments and modeling to determine the extent to which matrix heterogeneity disrupts the potential for cell sensing of a locally stiff feature in the matrix. Results showed that, at the scale of a single cell, spatial heterogeneity in local stiffness was larger than the increase in stiffness due to a stiff feature. The heterogeneity was reduced only for large length scales compared to the fiber length. Experiments verified this conclusion, showing spheroids of cells, which were large compared to the average fiber length, spreading preferentially toward stiff inclusions. Hence, the propagation of mechanical cues through the matrix depends on length scale, with single cells being able to sense only the stiffness of the nearby fibers and multicellular structures, such as tumors, also sensing the stiffness of distant matrix features. 
    more » « less
  2. null (Ed.)
    Through mechanical forces, biological cells remodel the surrounding collagen network, generating striking deformation patterns. Tethers—tracts of high densification and fibre alignment—form between cells, thinner bands emanate from cell clusters. While tethers facilitate cell migration and communication, how they form is unclear. Combining modelling, simulation and experiment, we show that tether formation is a densification phase transition of the extracellular matrix, caused by buckling instability of network fibres under cell-induced compression, featuring unexpected similarities with martensitic microstructures. Multiscale averaging yields a two-phase, bistable continuum energy landscape for fibrous collagen, with a densified/aligned second phase. Simulations predict strain discontinuities between the undensified and densified phase, which localizes within tethers as experimentally observed. In our experiments, active particles induce similar localized patterns as cells. This shows how cells exploit an instability to mechanically remodel the extracellular matrix simply by contracting, thereby facilitating mechanosensing, invasion and metastasis. 
    more » « less
  3. Abstract Fiber networks are the primary structural components of many biological structures, including the cell cytoskeleton and the extracellular matrix. These materials exhibit global nonlinearities, such as stiffening in extension and shear, during which the fibers bend and align with the direction of applied loading. Precise details of deformations at the scale of the fibers during strain stiffening are still lacking, however, as prior work has studied fiber alignment primarily from a qualitative perspective, which leaves incomplete the understanding of how the local microstructural evolution leads to the global mechanical behavior. To fill this gap, we studied how axial forces are transmitted inside the fiber network along paths called force chains, which continuously evolve during the course of deformation. We performed numerical simulations on two-dimensional networks of random fibers under uniaxial extension and shear, modeling the fibers using beam elements in finite element software. To quantify the force chains, we identified all chains of connected fibers for which the axial force was larger than a preset threshold and computed the total length of all such chains. To study the evolution of force chains during loading, we computed the derivative of the total length of all force chains with respect to the applied engineering strain. Results showed that the highest rate of evolution of force chains coincided with the global critical strain for strain stiffening of the fiber network. Therefore, force chains are an important factor connecting understanding of the local kinematics and force transmission to the macroscale stiffness of the fiber network. 
    more » « less
  4. Cells can sense and respond to mechanical forces in fibrous extracellular matrices (ECMs) over distances much greater than their size. This phenomenon, termed long-range force transmission, is enabled by the realignment (buckling) of collagen fibers along directions where the forces are tensile (compressive). However, whether other key structural components of the ECM, in particular glycosaminoglycans (GAGs), can affect the efficiency of cellular force transmission remains unclear. Here we developed a theoretical model of force transmission in collagen networks with interpenetrating GAGs, capturing the competition between tension-driven collagen fiber alignment and the swelling pressure induced by GAGs. Using this model, we show that the swelling pressure provided by GAGs increases the stiffness of the collagen network by stretching the fibers in an isotropic manner. We found that the GAG-induced swelling pressure can help collagen fibers resist buckling as the cells exert contractile forces. This mechanism impedes the alignment of collagen fibers and decreases long-range cellular mechanical communication. We experimentally validated the theoretical predictions by comparing the intensity of collagen fiber alignment between cellular spheroids cultured on collagen gels versus collagen–GAG cogels. We found significantly lower intensities of aligned collagen in collagen–GAG cogels, consistent with the prediction that GAGs can prevent collagen fiber alignment. The role of GAGs in modulating force transmission uncovered in this work can be extended to understand pathological processes such as the formation of fibrotic scars and cancer metastasis, where cells communicate in the presence of abnormally high concentrations of GAGs. 
    more » « less
  5. Fibrous networks such as collagen are common in physiological systems. One important function of these networks is to provide mechanical stability for cells and tissues. At physiological levels of connectivity, such networks would be mechanically unstable with only central-force interactions. While networks can be stabilized by bending interactions, it has also been shown that they exhibit a critical transition from floppy to rigid as a function of applied strain. Beyond a certain strain threshold, it is predicted that underconstrained networks with only central-force interactions exhibit a discontinuity in the shear modulus. We study the finite-size scaling behavior of this transition and identify both the mechanical discontinuity and critical exponents in the thermodynamic limit. We find both non-mean-field behavior and evidence for a hyperscaling relation for the critical exponents, for which the network stiffness is analogous to the heat capacity for thermal phase transitions. Further evidence for this is also found in the self-averaging properties of fiber networks. 
    more » « less