Strain-enhanced stress relaxation impacts nonlinearelasticity in collagen gelsSungmin Nama, Kenneth H. Hub, Manish J. Buttec, and Ovijit Chaudhuria,1

aDepartment of Mechanical Engineering, Stanford University, Stanford, CA 94305; bBiophysics Program, Stanford University, Stanford, CA 94305;and cDepartment of Pediatrics, Stanford University, Stanford, CA 94305

Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved April 4, 2016 (received for review December 3, 2015)

The extracellular matrix (ECM) is a complex assembly of structuralproteins that provides physical support and biochemical signaling tocells in tissues. Themechanical properties of the ECMhave been foundto play a key role in regulating cell behaviors such as differentiationand malignancy. Gels formed from ECM protein biopolymers such ascollagen or fibrin are commonly used for 3D cell culture models oftissue. One of the most striking features of these gels is that theyexhibit nonlinear elasticity, undergoing strain stiffening. However,these gels are also viscoelastic and exhibit stress relaxation, with theresistance of the gel to a deformation relaxing over time. Recentstudies have suggested that cells sense and respond to both nonlinearelasticity and viscoelasticity of ECM, yet little is known about theconnection between nonlinear elasticity and viscoelasticity. Here, wereport that, as strain is increased, not only do biopolymer gels stiffenbut they also exhibit faster stress relaxation, reducing the timescaleover which elastic energy is dissipated. This effect is not universal toall biological gels and is mediated through weak cross-links. Mecha-nistically, computational modeling and atomic force microscopy (AFM)indicate that strain-enhanced stress relaxation of collagen gels arisesfrom force-dependent unbinding of weak bonds between collagenfibers. The broader effect of strain-enhanced stress relaxation is torapidly diminish strain stiffening over time. These results reveal theinterplay between nonlinear elasticity and viscoelasticity in collagengels, and highlight the complexity of the ECM mechanics that arelikely sensed through cellular mechanotransduction.

collagen mechanics | viscoelasticity | force-dependent unbinding |biopolymers | stress relaxation

The composition and architecture of ECM is heterogeneous andvaries with tissue type and location. One particularly important

ECM protein is type Ι collagen, which is the most abundant ECMcomponent and primarily determines the mechanics of connectivetissue (1). Type 1 collagen self-assembles into fibers, and these fi-bers can form networks in vitro. Studies investigating the mechan-ical properties of collagen networks have revealed that thesenetworks are nonlinearly elastic and exhibit strain stiffening, or anincrease in the elasticity as the strain on the network is enhanced(1–3). This nonlinear elasticity is also a characteristic feature of fi-brin gels, which serve as the major component of blood clots, as wellas in reconstituted networks of intermediate filaments and cyto-skeletal actin networks (2, 4–7). These networks are all composed ofsemiflexible polymers or fibers, which are relatively rigid, so that thetangent to the contour of the polymer is correlated over longlengths, yet undergo substantial bending fluctuations due to thermalenergy. Semiflexible polymers or fibers form networks at low vol-ume fractions (8). Strain stiffening in these networks is thought toarise from either the entropic elasticity of single polymers resistingextension (entropic model) (2, 5), or from alignment of fibers in thedirection of strain with a corresponding transition to a regime ofelasticity dominated by fiber stretching at higher strains (non-entropic model) (5, 7, 9, 10). Although it has long been known thatcells sense and respond to the elastic modulus of ECMs (11–14),recent work has indicated an impact of nonlinear elasticity as well.Studies have found that the nonlinear elasticity of ECM regulatesmodes of cell motility (15) and differentiation of mesenchymal stem

cells (16), alters how far cells are able to sense into the ECM (17),and enables long-range mechanical signaling between cells (18).In addition to often displaying nonlinear elasticity, most biological

gels are viscoelastic and exhibit a time-dependent elastic modulus.These gels undergo stress relaxation in response to an applied strain:the initial stress resisting an applied strain decreases over time dueto reorganization processes that relax the stresses in the matrix. Inthe case of collagen gels typically used for in vitro studies, visco-elasticity and stress relaxation likely arise from unbinding of theweak interactions, such as hydrophobic and electrostatic forces,which hold the fibers in a network (19–21). Interestingly, recentstudies have found that viscoelasticity in synthetic hydrogels used ascell culture substrates can influence cell behaviors such as spreading,proliferation, and differentiation (22–25). The nonlinear elasticity ofcollagen and fibrin is dependent on the history of applied strains,indicating an influence of viscoelasticity on nonlinear elasticity (19).Here, we directly investigate the coupling between viscoelasticityand nonlinear elasticity for various gels, and find that increasedstrain leads to faster stress relaxation in collagen and fibrin gels. Incollagen gels, these results can be explained by force-dependentunbinding of cross-links, and indicate a mechanism whereby strainstiffening is rapidly dissipated.

ResultsSince strain stiffening is induced from increasing strain (2), we firstexamined the stress relaxation of collagen gels as a function of in-creasing shear strain (Fig. 1A). In a stress relaxation test, a constantstrain is applied to the gel, and the stress, directly proportional tothe shear modulus in this test, is measured over time. Stress re-laxation tests were conducted on collagen gels with various strainsusing a rheometer (Fig. 1B). Strikingly, normalization of the stress

Significance

The extracellular matrix is a complex assembly of structural pro-teins that provides physical support and biochemical signaling tocells within our tissues. One of the key structural components ofthe extracellular matrix is collagen, and matrices of collagen ex-hibit remarkable mechanical properties. Their resistance to de-formation is enhanced as deformation is increased over shorttimescales, a behavior termed strain stiffening, yet they exhibitsome characteristics of viscous fluids at longer timescales. Strik-ingly, we show that the strain stiffening of collagen matrices iscoupled with their liquid-like behavior: at greater deformations,these matrices become stiffer but then flow more rapidly to relaxthis increase in stiffness. These complex mechanical behaviors arelikely to be relevant to cellular interactions with these matrices.

Author contributions: S.N., M.J.B., and O.C. designed research; S.N. and K.H.H. performedresearch; S.N. contributed new reagents/analytic tools; S.N. and O.C. analyzed data; andS.N. and O.C. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. Email: chaudhuri@stanford.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1523906113/-/DCSupplemental.

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relaxation data with the initial values of stress for each strainrevealed an enhancement in the rate of stress relaxation as strainwas increased: higher strains led to faster relaxation (Fig. 1C). As theinitial strain rate applied to establish a constant strain varied forthese tests, stress relaxation tests with a constant strain rate wereconducted and demonstrated the same behavior (Fig. S1 A and B).Similar results were found at a higher concentration of collagen(Fig. S1E). The stress relaxation behavior cannot be explained byporoelastic effects, as poroelastic stress relaxation, arising fromwater migration out of the gel, requires a volumetric deformation ofthe material, whereas shear rheology imposes a volume-preservingdeformation on the gel (26). Consistent with the findings of thestress relaxation tests, creep tests, in which strain in response to aconstant stress is measured, indicated that material flow was en-hanced by increased stresses (Fig. S2). Additionally, frequency-dependent rheology tests demonstrate an increase in the lossmodulus at higher strains (Fig. S3A), so that enhanced stress orstrain generally induced increased viscous behaviors in the visco-elastic gels. To examine the implications of this strain-enhancedstress relaxation in collagen for nonlinear elasticity, the resultswere displayed isochronally (Fig. 1D). Immediately following theapplied strain, the elastic modulus increased significantly overstrain as consistent with previous reports (1–3). However, strainstiffening was substantially diminished within 1 s, and almost dis-appeared by 300 s, due to the strain-enhanced stress relaxation.After finding strain-enhanced relaxation of collagen gels, we in-

vestigated whether strain-enhanced stress relaxation is a commonbehavior of other viscoelastic gels. First, the strain dependency ofstress relaxation in fibrin gels, which form fiber networks similar tocollagen, was examined. Fibrin gels also showed strain-enhancedstress relaxation, as well as a corresponding decline of strain stiff-ening over time, similar to collagen (Fig. 2 A and B and Fig. S1 Cand D). Next, reconstituted basement membrane (rBM) matrix,a nonfibrillar matrix often used for 3D cell culture, was tested.Interestingly, although rBM matrix exhibited substantial stressrelaxation, stress relaxation rates were similar for all strains,

contrasting the behavior in collagen and fibrin gels (Fig. 2C). rBMmatrix also displayed strain stiffening (Fig. S3E), demonstrating thatstrain stiffening is not necessarily associated with strain-enhancedstress relaxation. Finally, strain dependence of stress relaxation inagarose and polyacrylamide, which have been used for cancerspheroid assays and as substrates for 2D culture of cells (27), re-spectively, were assessed. Both nanoporous hydrogels are almostpurely elastic, exhibiting very little stress relaxation across all strainsbelow the fracture strain (Fig. 2 D and E). A comparison of thedependence of the time constant of stress relaxation, defined as thetime over which the stress was relaxed halfway between its initialand equilibrium value (Fig. S4), on the strain highlighted the distinctclasses of behavior (Fig. 2F). The time constants for relaxation ofcollagen and fibrin markedly decreased as strain increased, whereasother materials exhibited a strain-independent stress relaxation.Next, we investigated the basis for strain-enhanced stress re-

laxation in collagen gels. The collagen gels are formed through weakcross-links between fibers, so we tested whether forming rigid co-valent cross-links would impact stress relaxation. Collagen gels co-valently cross-linked with glutaraldehyde (GTA) or transglutaminase(tTG) displayed a diminished degree of stress relaxation, althoughstrain enhanced stress relaxation was still observed (Fig. 3A and Figs.S5 A and B and S6 A and B). Similar results were found from testingof fibrin gels cross-linked with factor XIII (Fig. 3B and Figs. S5E andS6C). These suggest that strain-enhanced stress relaxation in fibrinand collagen are associated with weak cross-linking.

Fig. 1. Strain-enhanced stress relaxation impacts nonlinear elasticity in colla-gen gels. (A) Confocal microscope image of a collagen gel using an overlay ofimages taken with confocal reflectance microscopy. (Scale bar: 25 μm.) (B) Stressrelaxation tests on collagen with various strains. (Inset) A constant strain is ap-plied during a stress relaxation test. (C) Normalized stress relaxation tests ofcollagen gels at different strains. In a stress relaxation test, the stress is directlyproportional to the relaxation modulus. (D) Isochronal display of elastic modulusfrom the stress relaxation tests of different strains, showing the elastic modulusat each strain for the specific time points. Data are shown as mean ± SD; n = 5.

Fig. 2. Stress relaxation tests with various materials commonly used for cellculture reveal that only fibrin and collagen gels exhibit strain-enhanced stressrelaxation. (A) Stress relaxation tests at different strains for fibrin. (B) Iso-chronal display of elastic modulus for fibrin from stress relaxation tests ofdifferent strains. Data are shown as mean ± SD; n = 5. (C–E) Stress relaxationtests at different strains for polyacrylamide, agarose, and reconstituted base-ment membrane (rBM) matrix. Insets are all SEM images for each gel. (Scalebar: 1 μm.) (F) Normalized time constants of stress relaxation as a function ofthe normalized strain for the indicated materials. Strains were normalized bythe strain at which the maximum of shear storage modulus (G′max) is measuredin amplitude sweep, and time is normalized by the time constant for stressrelaxation at low strains imposed for each material (Figs. S5 and S6).

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To reveal other important factors underlying strain-enhancedstress relaxation, stress relaxation tests were applied sequentially.After one stress relaxation test had been conducted on a collagengel, an identical stress relaxation test was imposed again after the gelwas allowed to equilibrate (Fig. 3C, Inset). The initial elastic mod-ulus for the second step was dramatically reduced, indicating thatplastic deformation, or permanent remodeling of gel architecture,had occurred (Fig. 3C). Plasticity was assessed by visualizing andquantifying fiber orientation initially, under shear, and followingremoval of the shear (Fig. 3D and Fig. S7A). A change in orientationof the fibers is induced by shear, and the change is sustained fol-lowing removal of the imposed shear (Fig. 3 D and E), demon-strating plasticity. Next, a negative shear strain of the samemagnitude was applied without any equilibration time following aninitial stress relaxation test, and showed that the initial elasticmodulus decreased slightly compared with the first step (Fig. 3F).When equilibration time was allowed between the stress relaxationtests, however, the gel recovered an initial modulus that was similarto the original value (Fig. 3 G and H). Although fiber lengtheningmay occur and lead to relaxation of the gels during the stress re-laxation tests, self-assembly of the fibers is quenched by the time ofthe second test and the process of fiber lengthening is irreversible(19). Thus, the recovery of the modulus after an equilibration timeindicates that the stress relaxation response cannot be fully explainedby fiber lengthening. Instead, these results suggest a component offiber–fiber unbinding during the first stress relaxation test, followedby rebinding of fibers during the equilibration time, leading to the

recovery of the elastic modulus. Together, these results indicateaxially dependent reorganization of the networks and unbinding offibers due to a shear strain, followed by rebinding of fibers over time.One plausible explanation for the strain-enhanced stress re-

laxation behavior of collagen gels is that it arises from force-dependent unbinding of bonds between fibers (Fig. 4A). Whena strain is initially applied to the networks, individual fibers in thenetwork are strained and exert a force opposing the strain based ontheir force–extension relation, leading to strain stiffening due to thenonlinear elasticity of single filaments (entropic model) or alignmentof fibers in the direction of strain (nonentropic model) as has beenproposed previously (2, 7). Forces on the fibers are carried throughthe bonds that link the fibers together in the network. Following theBell model (28), we propose that unbinding of these links is forcedependent, and that a greater force leads to a higher probability ofunbinding. This force-dependent unbinding could lead to strain-enhanced stress relaxation: greater strains on the network lead tohigher forces carried by the fibers and thus higher forces on thebonds linking the fibers, which in turn leads to faster unbinding ofthe fibers. Unbound fibers do not carry any force, so that unbindingof a fiber leads to a decrease in stress and network elasticity. Shortertimescales of unbinding translate to faster relaxation of stresses inthe gel overall. Subsequently, we expect that unbound fibers canthen rejoin to the network in a more relaxed state. We used com-putational modeling to investigate the feasibility of the pro-posed mechanism in both entropic and nonentropic models ofnonlinear elasticity. Force-dependent unbinding and fiber rebinding

Fig. 3. Stress relaxation is associated with a weak cross-linking, axial dependent reorganization, and rebinding of fibers to the networks. Stress relaxation tests for(A) collagen, and (B) fibrin with andwithout covalent cross-linking. For cross-linking, collagenwas treated by GTA and fibrin containing factor XIII was used. Data areshown as mean ± SD; n = 5. (C) Results for two sequential stress relaxation tests with identical positive strains. (D) The polar distribution of angles of collagen fibersin the network initially (Left), under shear (Center), and following removal of the imposed shear (Right). (E) A comparison of the averaged orientation of collagenfibers in the network, corresponding to the conditions in D. Data are shown as mean ± SEM; n = 387–439. (F) Multiple-stepwise stress relaxation test with a positivestrain followed immediately by a test with a negative strain of the same magnitude, and (G) a stress relaxation test with a positive strain followed by a test with anegative strain of the same magnitude following an equilibration time. (H) A comparison of the recovery of the elastic modulus in a negative strain stress relaxationtest following a positive stress relaxation test with or without an equilibration time. G1 and G2 represent the initial elastic modulus starting with stress relaxation.Data are shown as mean ± SD; n = 5. *P < 0.05; **P < 0.01; ****P < 0.0001 (Student’s t test). Insets are all schematics that describe the procedure for multiple stressrelaxation tests. Red lines represent the first step of stress relaxation, and blue ones represent the successive stress relaxation.

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were incorporated into previously established time-independentmodels (2, 7) for nonlinear elasticity in biological gels (SI Materialsand Methods and Fig. S8). Force-dependent unbinding probabilityof fibers was incorporated through the following modification ofthe Bell model (28):

dpbdt

= kbð1− pbÞ− ku   pb   e

�fγckBT

�

, [1]

where pb is the probability of a given fiber in the network beingbound and kb and ku are constants for binding and unbinding prob-ability, f is the force on a single fiber, and γc is a constant represent-ing bond strength (SI Materials and Methods). Unbound fibers areassumed to have a constant probability of rebinding to the networksin a more relaxed state (SI Materials and Methods). With theseinputs, the simulations of stress relaxation of fiber networks underdifferent strains displayed the experimentally observed strain-enhanced stress relaxation behavior of collagen gels in both theentropic and nonentropic models (Fig. 4 B and C). When the force-dependent unbinding model was implemented without rebindingof fibers, the elastic moduli collapsed faster than those of experi-ments in both the entropic and nonentropic models (Fig. 4 D andE). This suggests that fiber rebinding may account for the nonzeroequilibrium moduli that were experimentally observed (Fig. S1F).Alternatively, when both models were implemented with a proba-bility of unbinding that is force independent, the simulations showedthat stress relaxation became independent of strain, reminiscent ofthe behavior of rBM gels (Fig. 4 F and G). Taken together, thesesimulations indicate that force-dependent unbinding followed by

rebinding of fibers can explain strain-enhanced stress relaxation incollagen networks.To directly verify the proposed molecular mechanism of force-

dependent unbinding of fibers in collagen gels, the lifetimes ofcollagen fiber attachments under different forces were measuredusing atomic force microscopy (AFM) (Fig. 5A). First, collagenfibers were bound to AFM cantilever tips functionalized with a typeI collagen antibody (SI Materials and Methods and Fig. S9A). Next,the collagen-coated AFM tips were indented into collagen gels, toinitiate binding between collagen fibers on the tip and in the gel,and then constant tensile forces were exerted on these attachmentsuntil the attachments were ruptured. The lifetimes of the attach-ments were determined from these curves and found to decay ex-ponentially with an increase in the clamping force (Fig. 5 B and C).Although the architecture of interactions between collagen fiberson the AFM cantilever and the surface of the collagen gel might notcapture the interactions of collagen fibers that are polymerizedtogether in the gel, the fundamental bonding mechanism betweencollagen fibers is expected to be similar. These results directlydemonstrate the force dependence of unbinding of collagen fibers.

Discussion and ConclusionIn summary, collagen and fibrin gels stiffen as strained, but thestrain stiffening is diminished over time due to strain-enhancedstress relaxation. Both entropic and nonentropic models of collagennetwork mechanics reveal that force-dependent unbinding betweenfibers leads to strain-enhanced stress relaxation, and AFM experi-ments confirm the presence of force-dependent unbinding betweencollagen fibers. We note that previous results have implicated therole of intrafibrillar lengthening in stress relaxation (19, 29, 30).

Fig. 4. Force-dependent unbinding of fibers leads to strain–enhanced stress relaxation in fiber networks. (A) Schematic of the proposed mechanism underlyingstrain-enhanced stress relaxation. Under strain imposed during a stress relaxation test, fibers in the network are strained and exert a force resisting the straindetermined by the fiber’s force–extension relaxation. These forces are transmitted through cross-link points linking the fibers together. It is hypothesized that theprobability of unbinding or cross-link disassociation is force dependent, or a higher force leads to a greater probability of unbinding for a fiber. This is predicted tolead to strain-enhanced stress relaxation. Unbound fibers can rebind to the networks, contributing the elastic modulus again. Comparison of stress relaxation datafrom experiments (exp, dotted line) and the corresponding results from the computational simulations (sim, solid line) of (B) the entropic model and (C) thenonentropic model for various strains. Simulation results given the assumptions that there is no rebinding of fibers to the networks for (D) the entropic model and(E) nonentropic model or that the probability of binding is independent of the force for (F) the entropic model and (G) nonentropic model.

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However, intrafibrillar stress relaxation cannot explain the recoveryof elastic modulus in double stress relaxation tests because theprocess of fiber lengthening is irreversible (Fig. 3 F and G). Fur-thermore, fiber lengthening cannot account for the permanentchange in orientation of the fibers when the strain is removed whileunbinding of fibers from one another, followed by reorientation ofthe fiber, and rebinding can (Fig. 3 D and E). Together, these in-dicate the force-dependent unbinding of fibers as the molecularmechanism underlying the observed behavior of strain-enhancedstress relaxation. However, it is likely that intrafibrillar lengthening,arising from sliding of fibrils relative to one another within a fiber,plays a role in the bulk stress relaxation tests reported here. It ispossible that intrafibrillar lengthening may dominate the stress re-laxation response at longer timescales over which the predictionsfrom models based on force-dependent unbinding of fibers deviatesfrom the experimental results (Fig. S10).The viscoelastic behavior of collagen networks observed in this

study contrasts with that of cross-linked actin networks. Actin is anintracellular semiflexible biopolymer, and cross-linked actin net-works exhibit strain stiffening as does collagen (2, 5). A recent studyexamined the viscoelasticity of actin networks cross-linked by heavymeromyosin both experimentally and computationally (31). In re-sponse to a strain impulse, actin networks undergo fluidization, or adecrease in the elastic modulus and increase in the viscous modulus,followed by a full recovery of the initial properties. These resultswere modeled using a glassy worm-like chain model of actin, whichaccounts for the caging and enthalpic trapping of a worm-like chainpolymer in a network by expanding the relaxation time modes ofthe worm-like chain (32), combined with reversible force-dependentbonds between the filaments. This model captured the experi-mentally observed behavior of fluidization and recovery in the actinnetworks. In contrast to the actin networks, collagen gels do notfully recover following fluidization and exhibit substantial plasticity(Fig. 3 D and E), highlighting the distinct behaviors between cross-linked actin networks and collagen gels (Fig. S11). However, weexpect that incorporation of the glassy worm-like chain model intoour entropic model of collagen network viscoelasticity that includesirreversible force-dependent bonds would result in a prediction ofstrain-enhanced stress relaxation, as fiber bonds in this model wouldalso carry increased force at higher strains.For 3D cell culture experiments using collagen gels as ECM,

these results suggest that the effect of mechanical properties of theECM on cells may be highly dependent on the strain that cells exert,timescales over which cells sense mechanical cues, and the cross-linking state of the matrix. Although the higher the strain that cells

exert on these matrices the higher the resistance cells encounter, theresistance of the ECM is relaxed rapidly due to strain-enhancedstress relaxation. The timescale for the cell–extracellular matrix in-teractions underlying mechanotransduction spans several orders ofmagnitude of time. Cells are able to bind to ECM over a timescaleof ∼1 s (12), exert forces, and form stable adhesions on a timescaleof minutes (23), and undergo cell spreading on a timescale of hours(33). These timescales fall within the range of time over whichstrain-enhanced stress relaxation is observed. Furthermore, cells on2D substrates (34) and in 3D collagen gels (35) can exert strains ofup to 0.5 and stresses on the order of 100–1,000 Pa (36), which arewithin the range of strains and stresses imposed and measured inour stress relaxation tests (Fig. 1B). Therefore, due to the overlap intimescales, levels of stress, and levels of strain between the regimeover which strain-enhanced stress relaxation is observed with thoserelevant to cell–ECM interactions, it is expected that strain-enhanced stress relaxation impacts cell–ECMmechanotransduction.It was found that a greater degree of covalent cross-linking reducedthe degree of stress relaxation in matrices. Interestingly, strain-enhanced stress relaxation is still observed in the presence of co-valent cross-links, although the degree of stress relaxation is reduced(Fig. S6). Even in the case of fully cross-linked networks, cells secreteproteases to degrade collagen networks, possibly enhancing stressrelaxation of the matrix adjacent to the cell (37).There is some evidence that strain-enhanced stress relaxation

behavior in collagen networks may be relevant to bulk tissue me-chanics. Collagen fiber networks in skin exhibit plastic deformationunder tensile loading due to slipping of collagen fibers (38), andsliding of collagen is observed in developing tendon (39), indicatingthe physiological relevance of weak bonds in collagen. However,one commonly used model of tissue biomechanics is the quasilinearviscoelastic model introduced by Fung (40), which decouples thecontribution of the strain-dependent and time-dependent compo-nents of the stress relaxation response. In contrast, we have foundthat there is coupling between the strain- and time-dependentcomponents of the response in in vitro collagen gels, as the time-scale for relaxation is strain dependent. It is possible that this dif-ference could be explained by the different structural compositionof in vivo tissues, as tissues consist of various other structuralcomponents including elastin (38), and exhibit different levelsof covalent cross-linking (41). Alternatively, another explanationcould be in the standard practice of preconditioning biologicaltissues, or exerting stress–strain cycles on the tissue until the ob-served stress–strain curve is repeatable, before measurements arerecorded and analyzed. The process of preconditioning may breakthe weak bonds in the collagen networks. Indeed, a study of pre-conditioning found it to be associated with enhanced collagen fiberalignment (42). There are some studies that have reported strain-enhanced stress relaxation in tissues such as ligaments and tendon(43, 44), although the mechanism of strain-enhanced relaxationunderlying this tissue-scale behavior was not established.Although the stiffness of ECM has been characterized in various

contexts, these results highlight the complex viscoelastic propertiesof ECM at the microscale. Collagen networks strain stiffen, but thedegree of strain stiffening is diminished over time due to strain-enhanced stress relaxation. Elucidating the complex mechanicalbehaviors in the ECMmay be critical to understanding the how themechanics of the ECM regulates cell behaviors.

Materials and MethodsMaterials Preparation. All gels were formed between the rheometer plates.Collagen type Ι (Corning) was diluted at 4 °C by 10× and 1× DMEM to reach afinal concentration of 1 mg/mL, and pH was adjusted to 8.5 by adding 1 MNaOH, and immediately deposited on the rheometer plates. Polymerization ofcollagen was initiated by heating the solution to 37 °C. Matrigel (Corning) wasused as rBM matrix at a concentration of 9.2 mg/mL The gelation of rBM wasalso initiated by heating to 37 °C. Low gelling temperature Agarose (Sigma)was dissolved into 1× DMEM to a concentration of 1% (wt/vol) at a pH of 7.4.

Fig. 5. Force-clamp spectroscopy validates force-dependent unbinding on thecollagen networks. (A) Schematic of the force-clamp spectroscopy: AFM canti-lever tips (black) functionalized with collagen type Ι antibodies (blue) andcollagen fibers (red) are indented and then retracted from a collagen gel (red).(B) Typical raw data obtained in AFM force-clamp experiments. After a smallconstant compressional force is applied, the AFM tip was retracted and held atdifferent tensional forces on the attachment until the attachment was broken.(C) The averaged lifetimes of attachments between fibers as a function oftensional force. Blue line indicates the best-fit exponential function to the data.Green boxes indicate the lifetime measurements from the initial force-clampexperiments using an antibody-only coated cantilever, before the collagen fi-bers are attached to the cantilever. Data are shown as mean ± SD; n = 40.

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The solid agarose was heated before use so that it forms a liquid and thencooled to 25 °C to solidify. The polyacrylamide gel was prepared by mixingacrylamide [3% (vol/vol)] and bis-acrylamide (0.15%) with tetramethylethyle-nediamine and ammonia persulfate following standard methods (45). Forpreparation of fibrin gel with cross-linking, 2 mg/mL human fibrinogen withfactor XΙΙΙ diluted by 50 mM Tris·HCl buffer (7) at pH 7.4, containing 150 mMNaCl and 10 mM CaCl2, was mixed with human thrombin to a final concen-tration of 0.6 U/mL. To purify the fibrinogen of factor XΙΙΙ, human fibrinogendepleted of plasminogen, von Willebrand factor, and fibronectin (EnzymeResearch Laboratories) was passed through an affinity column containing anantibody to factor XΙΙΙ (Affinity Biologicals) coupled to the CNBr Sepharose(Sigma) following a previously published method (19). To cross-link collagennetworks covalently, a solution of 0.2% GTA (Sigma) in 1× DMEM was de-posited around the collagen gel between the rheometer plates, after collagenhave polymerized for at least 20 min. The GTA was allowed to diffuse into thecollagen gel and cross-link it for 2 h before mechanical testing. After 2 h, thestorage modulus of the collagen gels cross-linked by GTA was equilibrated.Collagen gels were also cross-linked with tTG (Sigma). The tTG was pretreatedin 2 mM DTT in 50 mM Tris buffer (pH 7.4) for 10 min at room temperaturebefore adding to a final buffer containing 5 mM CaCl2. Collagen stock solutionwas mixed with 2 mM DTT and 5 mM CaCl2 in 50 mM Tris buffer to a finalweight ratio between collagen and tTG of 50:1 (wt/wt). The storage modulusdid not reach an equilibrium value for collagen gels cross-linked with tTG, sostress relaxation tests were all conducted after 5 h of cross-linking.

Measurement of Stress Relaxation. Rheology measurements of stress relaxationwere performed using an AR-G2 stress-controlled rheometer (TA Instruments)equippedwith 25-mmtop- andbottom-plate geometry. Plateswith stainless-steel

surfaces were used for all of the materials except for collagen, as collagen gelswere found to slip on the stainless-steel surface. To enhance the attachment ofcollagen to the surface, 25-mm poly-L-lysine–coated coverslips (Neuvitro Corpo-ration) were glued to the surface. With this attachment, slipping of collagenagainst the surface was prevented. All materials were deposited onto the bot-tom plate of the rheometer immediately before gelation, and the top plate waslowered rapidly so that the gel formed a uniform disk between the two plates.To prevent dehydration of samples, the exposed gel surfaces within the rhe-ometer geometry were coated with mineral oil (Sigma), except for the cross-linked collagen. Gelation was monitored with continuous oscillations at a strainof 0.01 and frequency of 1 rad/s, and mechanical tests were conducted once thestorage modulus reached an equilibrium value; for stress relaxation tests, strainswere applied with a rise time of 0.1 s, except for experiments with a constantstrain rate. For the stress relaxation tests at different strain values, only one stressrelaxation test is conducted on any given sample. For the double stress relaxationtests, the first strain is applied for 5 min on a fresh, previously unstrained sample,followed by a recovery time of 0–5 min, and subsequently the second strain isapplied for another 5 min.

ACKNOWLEDGMENTS. We acknowledge the help of Joanna Lee and KatrinaWisdom for discussions and technical assistance, Marc Levenston for discus-sions and use of rheometer, Stephan Munster for guidance on collagen gelattachment, and David Mooney (Harvard University) for review of themanuscript. This work was supported by the Jeongsong Cultural Foundationand Samsung Scholarship (to S.N.); NIH/NIGMS Grant R01 GM110482, NSF GrantCBET 1264833, and Stanford Child Health Research Institute grants (to M.J.B.);and DARPA Grant D14AP00044 (to O.C.).

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