Micro-Tensile Rheology of Fibrous Gels Quantifies Strain-dependent Anisotropy

Biological semiflexible fibrous hydrogels facilitate the integrity and flexibility of soft tissues [1]. Fiber networks such as collagen compose the extra-cellular matrix (ECM), providing mechanical cues that guide cell migration, maturation and morphology [2], [3], [4]. Cells can remodel their surrounding ECM by its digestion [5], secretion [6] and by applying contractile forces that deform it [7]. Thus, tissue homeostasis is achieved by a feedback loop between cell activity and matrix mechanics [8,9]. In particular, cell-ECM mechanical interactions play a crucial role in morphogenesis [10], wound healing [11,12] and cancer metastasis [13], [14], [15].

Semiflexible fiber gels such as collagen and fibrin exhibit unique mechanical properties. The mechanics of individual semiflexible fibers are well explained by the worm-like chain model, describing them as elastic beams subject to thermal bending fluctuations [16,17]. Crosslinked gels of collagen and fibrin show dramatic strain-stiffening [18,19], arising from the stiffening of tensed fibers and the buckling of compressed fibers. Extensive research characterized their bulk rheology properties, including the dependence on concentration [17,19], preparation conditions [20,21], prestress [22,23], and plasticity [24]. Bulk rheology, however, falls short of characterizing the fibrous gel mechanics at the microscale, at which cells sense and modify the gel, including its local heterogeneity and anisotropy.

Microrheology, and in particular optical tweezers microrheology, has proven to be an invaluable tool in addressing these microscale aspects. It uses a tightly focused laser beam to manipulate micron-sized beads, thereby probing the heterogeneous stiffness and anisotropy of fibrous gels within a 3D microenvironment [25], [26], [27]. Active microrheology has been utilized to characterize the stiffness changes near cells [25,28,29] and tumors [15], and showed that cells greatly stiffen their local environment by aligning the ECM fibers [7,30]. In particular, pairs of cells and cell aggregates that are located close to one another tend to form a “band” of dense and aligned fibers between them [31], [32], [33], [34]. These bands were shown to be anisotropic, and to persist even when cell-induced forces are removed [35]. Such local stiffening and anisotropy also modify force propagation in the network between cells [36], [37], [38], and thus can regulate the mechanical interaction between cells, relevant to tissue morphogenesis and development [12,13].

Despite the accumulated knowledge on the micromechanics of semiflexible fiber gels, microrheology normally lacks a mechanical control variable such as strain. Consequently, microrheology has rarely been used to quantitatively study nonlinear mechanics at large deformations. To address this gap, we introduce a unique experimental setup that we term “Micro-Tensile Rheology”. It enables us to measure the local stiffness and anisotropy of fibrous gels under well-defined and externally controlled deformations. Our setup combines mechanical gel stretching with active microrheology and confocal fluorescence microscopy. We use it to quantify the mechanical changes in gels of collagen and fibrin under tension, simultaneously measuring both stiffening and strain. Furthermore, we measure the stiffness and anisotropy between pairs of contractile cancer-cell aggregates, and evaluate the similarity and differences between the tension applied by the stretching apparatus and that applied by cancer cells. Our work complements current state-of-the-art studies, which used different methods to mechanically perturb gels [39], [40], [41], and differs from them in that it allows gradual, well-controlled deformations, describing the stiffening process in greater detail.

Our findings show considerable stiffening already at relatively low strains of several percent, with a moderate stiffness anisotropy. We also show that along bands of aligned fibers between cancer cell aggregates, similar, but somewhat higher stiffening and anisotropy occur compared to gels deformed by the stretching apparatus. These findings can help illuminate the mechanical cues in the tumor microenvironment. Furthermore, they may help in evaluating the validity of models offered in the literature. A better understanding of such systems can also aid in programming the mechanics of engineered tissues.

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