The stiffness of a network of fibers impacts how cells sense and respond to the surrounding matrix, but the complicated mechanics of fibrous materials make it unclear as to what stiffness a cell would sense. Here, we consider three different factors that may affect the stiffness at the scale of a cell. First, the random structure of the fiber network produces local heterogeneities in both displacements and stiffness. Secondly, alignment of fibers, as is common in biological tissues, creates mechanical anisotropy. Thirdly, stresses and displacements propagate over a long range in fibrous materials, suggesting that mechanical cues from rigid or compliant inclusions may increase or decrease the stiffness over long distances. To quantify effects of these three factors on stiffness at the scale of a cell, we use a combination of experiments and modeling. Our experiments mimic the local contractile forces of a cell by using particles made of poly(N-isopropylacrylamide), a hydrogel that contracts when heated. By embedding particles made of this gel into networks of fibrous collagen I and controlling the temperature, we generate well-controlled local displacements that we quantify with digital image correlation. Our theoretical model treats each fiber as a beam that can bend, stretch, and buckle. The results show that the random fibrous structure produces local moduli that vary by a factor of three. The presence of rigid inclusions in the matrix can further amplify heterogeneities in local stiffness. Anisotropy due to alignment of fibers has a far larger effect, with modulus in the direction of fiber alignment being an order of magnitude larger than in the direction perpendicular to fiber alignment. These findings suggest that the stiffness of a cell‚Äôs environment may be more complicated than previously thought, emphasizing the need for considering heterogeneity and anisotropy in studies of cell-matrix interactions.

Stiffness at the scale of a cell in a heterogeneous fibrous matrix

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