Research on soft materials, including colloidal suspensions, glasses, pastes, emulsions, foams, polymer networks, liquid crystals, granular materials, and cells, has captured the interest of scientists and engineers in fields ranging from physics and chemical engineering to materials science and cell biology. Recent advances in rheological methods to probe mechanical responses of these complex media have been instrumental for producing new understanding of soft matter and for generating novel technological applications. This review surveys these technical developments and current work in the field, with partial aim to illustrate open questions for future research.

Many biomaterials formed by crosslinked semiflexible or rigid filaments exhibit non-linear rheology in the form of strain-stiffening and negative normal stress when samples are deformed in simple shear geometry. Two different classes of theoretical models have been developed to explain this non-linear elastic response, which is neither predicted by rubber elasticity theory nor observed in elastomers or gels formed by flexible polymers. One model considers the response of isotropic networks of semiflexible polymers that have non-linear force-elongation relations arising from their thermal fluctuations. The other considers networks of rigid filaments with linear force-elongation relations in which non-linearity arises from non-affine deformation and a shift from filament bending to stretching at increasing strains. Fibrin gels are a good experimental system to test these theories because the fibrin monomer assembles under different conditions to form either thermally fluctuating protofibrils with persistence length on the order of the network mesh size, or thicker rigid fibers. Comparison of rheologic and optical measurements shows that strain stiffening and negative normal stress appear at smaller strains than those at which filament orientation is evident from birefringence. Comparisons of shear to normal stresses and the strain-dependence of shear moduli and birefringence suggest methods to evaluate the applicability of different theories of rod-like polymer networks. The strain-dependence of the ratio of normal stress to shear stress is one parameter that distinguishes semi-flexible and rigid filament models, and comparisons with experiments reveal conditions under which specific theories may be applicable.

Recent observations suggest that cells on fibrous extracellular matrix materials sense mechanical signals over much larger distances than they do on linearly elastic synthetic materials. In this work, we systematically investigate the distance fibroblasts can sense a rigid boundary through fibrous gels by quantifying the spread areas of human lung fibroblasts and 3T3 fibroblasts cultured on sloped collagen and fibrin gels. The cell areas gradually decrease as gel thickness increases from 0 to 150 μm, with characteristic sensing distances of >65 μm below fibrin and collagen gels, and spreading affected on gels as thick as 150 μm. These results demonstrate that fibroblasts sense deeper into collagen and fibrin gels than they do into polyacrylamide gels, with the latter exhibiting characteristic sensing distances of <5 μm. We apply finite-element analysis to explore the role of strain stiffening, a characteristic mechanical property of collagen and fibrin that is not observed in polyacrylamide, in facilitating mechanosensing over long distances. Our analysis shows that the effective stiffness of both linear and nonlinear materials sharply increases once the thickness is reduced below 5 μm, with only a slight enhancement in sensitivity to depth for the nonlinear material at very low thickness and high applied traction. Multiscale simulations with a simplified geometry predict changes in fiber alignment deep into the gel and a large increase in effective stiffness with a decrease in substrate thickness that is not predicted by nonlinear elasticity. These results suggest that the observed cell-spreading response to gel thickness is not explained by the nonlinear strain-stiffening behavior of the material alone and is likely due to the fibrous nature of the proteins.

Mechanical properties of cells and extracellular matrix (ECM) play important roles in many biological processes including stem cell differentiation, tumor formation, and wound healing. Changes in stiffness of cells and ECM are often signs of changes in cell physiology or diseases in tissues. Hence, cell stiffness is an index to evaluate the status of cell cultures. Among the multitude of methods applied to measure the stiffness of cells and tissues, micro-indentation using an Atomic Force Microscope (AFM) provides a way to reliably measure the stiffness of living cells. This method has been widely applied to characterize the micro-scale stiffness for a variety of materials ranging from metal surfaces to soft biological tissues and cells. The basic principle of this method is to indent a cell with an AFM tip of selected geometry and measure the applied force from the bending of the AFM cantilever. Fitting the force-indentation curve to the Hertz model for the corresponding tip geometry can give quantitative measurements of material stiffness. This paper demonstrates the procedure to characterize the stiffness of living cells using AFM. Key steps including the process of AFM calibration, force-curve acquisition, and data analysis using a MATLAB routine are demonstrated. Limitations of this method are also discussed. Video LinkThe video component of this article can be found at

Cell types from many tissues respond to changes in substrate stiffness by actively remodeling their cytoskeletons to alter spread area or adhesion strength, and in some cases changing their own stiffness to match that of their substrate. These cell responses to substrate stiffness are linked to substrate-induced changes in the state, localization, and amount of numerous proteins, but detailed evidence for the requirement of specific proteins in these distinct forms of mechanical response are scarce. Here we use microfluidics techniques to produce gels with a gradient of stiffness to show the essential function of filamin A in cell responses to mechanical stimuli and dissociate cell spreading and stiffening by contrasting responses of a pair of human melanoma-derived cell lines that differ in expression of this actin cross-linking protein. M2 melanoma cells null for filamin A do not alter their adherent area in response to increased substrate stiffness when they link to the substrate only through collagen receptors, but change adherent area normally when bound through fibronectin receptors. In contrast, filamin A-replete A7 cells change adherent area on both substrates and respond more strongly to collagen I-coated gels than to fibronectin-coated gels. Strikingly, A7 cells alter their stiffness, as measured by atomic force microscopy, to match the elastic modulus of the substrate immediately adjacent to them on the gradient. M2 cells, in contrast, maintain a constant stiffness on all substrates that is as low as that of A7 cells on the softest gels examined (1000 Pa). Comparison of cell spreading and cell stiffening on the same gradient substrates shows that cell spreading is uncoupled from stiffening. At saturating collagen and fibronectin concentrations, adhesion of M2 cells is reduced compared to that of A7 cells to an extent approximately equal to the difference in adherent area. Filamin A appears to be essential for cell stiffening on collagen, but not for cell spreading on fibronectin. These results have implications for different models of cell protrusion and adhesion and identify a key role for filamin A in altering cellular stiffness that cannot be compensated for by other actin cross-linkers in vivo.