Stiffening of Individual Fibrin Fibers Equitably Distributes Strain and Strengthens Networks

As the structural backbone of blood clots, fibrin networks carry out the mechanical task of stemming blood flow at sites of vascular injury. These networks exhibit a rich set of remarkable mechanical properties, but a detailed picture relating the microscopic mechanics of the individual fibers to the overall network properties has not been fully developed. In particular, how the high strain and failure characteristics of single fibers affect the overall strength of the network is not known. Using a combined fluorescence/atomic force microscope nanomanipulation system, we stretched 2-D fibrin networks to the point of failure, while recording the strain of individual fibers. Our results were compared to a pair of model networks: one composed of linearly responding elements and a second of nonlinear, strain-stiffening elements. We find that strain-stiffening of the individual fibers is necessary to explain the pattern of strain propagation throughout the network that we observe in our experiments. Fiber strain-stiffening acts to distribute strain more equitably within the network, reduce strain maxima, and increase network strength. Along with its physiological implications, a detailed understanding of this strengthening mechanism may lead to new design strategies for engineered polymeric materials.     

Mapping the depth dependence of shear properties in articular cartilage

Determining the depth dependence of the shear properties of articular cartilage is essential for understanding the structure-function relation in this tissue. Here, we measured spatial variations in the shear modulus G of bovine articular cartilage using a novel technique that combines shear testing, confocal imaging and force measurement. We found that G varied by up to two orders of magnitude across a single sample, exhibited a global minimum 50-250 microm below the articular surface in a region just below the superficial zone and was roughly constant at depths > 1000 microm (the "plateau region"). For plateau strains gamma(plateau) approximately 0.75% and overall compressive strains epsilon approximately 5%, G(min) and G(plateau) were approximately 70 and approximately 650 kPa, respectively. In addition, we found that the shear modulus profile depended strongly on the applied shear and axial strains. The greatest change in G occurred at the global minimum where the tissue was highly nonlinear, stiffening under increased shear strain, and weakening under increased compressive strain. Our results can be explained through a simple thought model describing the observed nonlinear behavior in terms of localized buckling of collagen fibers and suggest that compression may decrease the vulnerability of articular cartilage to shear-induced damage by lowering the effective strain on individual collagen fibrils.     

Nonlinear Mechanical Properties of Prestressed Branched Fibrous Networks

Random fiber networks constitute the solid skeleton of many biological materials such as the cytoskeleton of cells and extracellular matrix of soft tissues. These random networks show unique mechanical properties such as nonlinear shear strain-stiffening and strain softening when subjected to preextension and precompression, respectively. In this study, we perform numerical simulations to characterize the influence of axial prestress on the nonlinear mechanical response of random network structures as a function of their micromechanical and geometrical properties. We build our numerical network models using the microstructure of disordered hexagonal lattices and quantify their nonlinear shear response as a function of uniaxial prestress strain. We consider three different material models for individual fibers and fully characterize their influence on the mechanical response of prestressed networks. Moreover, we investigate both the influence of geometric disorder keeping the network connectivity constant and the influence of the randomness in the stiffness of individual fibers keeping their mean stiffness constant. The effects of network connectivity and bending rigidity of fibers are also determined. Several important conclusions are made, including that the tensile and compressive prestress strains, respectively, increase and decrease the initial network shear stiffness but have no effect on the maximal shear modulus. We discuss the findings in terms of microstructural properties such as the local strain energy distribution.     

Fibrin-fiber architecture influences cell spreading and differentiation

ABSTRACT

The mechanical and structural properties of the extracellular matrix (ECM) play an important role in regulating cell fate. The natural ECM has a complex fibrillar structure and shows nonlinear mechanical properties, which are both difficult to mimic synthetically. Therefore, systematically testing the influence of ECM properties on cellular behavior is very challenging. In this work we show two different approaches to tune the fibrillar structure and mechanical properties of fibrin hydrogels. Addition of extra thrombin before gelation increases the protein density within the fibrin fibers without significantly altering the mechanical properties of the resulting hydrogel. On the other hand, by forming a composite hydrogel with a synthetic biomimetic polyisocyanide network the protein density within the fibrin fibers decreases, and the mechanics of the composite material can be tuned by the PIC/fibrin mass ratio. The effect of the changes in gel structure and mechanics on cellular behavior are investigated, by studying human mesenchymal stem cell (hMSC) spreading and differentiation on these gels. We find that the trends observed in cell spreading and differentiation cannot be explained by the bulk mechanics of the gels, but correlate to the density of the fibrin fibers the gels are composed of. These findings strongly suggest that the microscopic properties of individual fibers in fibrous networks play an essential role in determining cell behavior.     

Contribution of collagen fibers to the compressive stiffness of cartilaginous tissues

Cartilaginous tissues such as the intervertebral disk are predominantly loaded under compression. Yet, they contain abundant collagen fibers, which are generally assumed to contribute to tensile loading only. Fiber tension is thought to originate from swelling of the proteoglycan-rich nucleus. However, in aged or degenerate disk, proteoglycans are depleted, whereas collagen content changes little. The question then rises to which extend the collagen may contribute to the compressive stiffness of the tissue. We hypothesized that this contribution is significant at high strain magnitudes and that the effect depends on fiber orientation. In addition, we aimed to determine the compression of the matrix. Bovine inner and outer annulus fibrosus specimens were subjected to incremental confined compression tests up to 60 % strain in radial and circumferential direction. The compressive aggregate modulus was determined per 10 % strain increment. The biochemical composition of the compressed specimens and uncompressed adjacent tissue was determined to compute solid matrix compression. The stiffness of all specimens increased nonlinearly with strain. The collagen-rich outer annulus was significantly stiffer than the inner annulus above 20 % compressive strain. Orientation influenced the modulus in the collagen-rich outer annulus. Finally, it was shown that the solid matrix was significantly compressed above 30 % strain. Therefore, we concluded that collagen fibers significantly contribute to the compressive stiffness of the intervertebral disk at high strains. This is valuable for understanding the compressive behavior of collagen-reinforced tissues in general, and may be particularly relevant for aging or degenerate disks, which become more fibrous and less hydrated.     

Normal and Fibrotic Rat Livers Demonstrate Shear Strain Softening and Compression Stiffening: A Model for Soft Tissue Mechanics

Tissues including liver stiffen and acquire more extracellular matrix with fibrosis. The relationship between matrix content and stiffness, however, is non-linear, and stiffness is only one component of tissue mechanics. The mechanical response of tissues such as liver to physiological stresses is not well described, and models of tissue mechanics are limited. To better understand the mechanics of the normal and fibrotic rat liver, we carried out a series of studies using parallel plate rheometry, measuring the response to compressive, extensional, and shear strains. We found that the shear storage and loss moduli G’ and G” and the apparent Young''s moduli measured by uniaxial strain orthogonal to the shear direction increased markedly with both progressive fibrosis and increasing compression, that livers shear strain softened, and that significant increases in shear modulus with compressional stress occurred within a range consistent with increased sinusoidal pressures in liver disease. Proteoglycan content and integrin-matrix interactions were significant determinants of liver mechanics, particularly in compression. We propose a new non-linear constitutive model of the liver. A key feature of this model is that, while it assumes overall liver incompressibility, it takes into account water flow and solid phase compressibility. In sum, we report a detailed study of non-linear liver mechanics under physiological strains in the normal state, early fibrosis, and late fibrosis. We propose a constitutive model that captures compression stiffening, tension softening, and shear softening, and can be understood in terms of the cellular and matrix components of the liver.     

Material properties of the human lumbar facet joint capsule

The human facet joint capsule is one of the structures in the lumbar spine that constrains motions of vertebrae during global spine loading (e.g., physiological flexion). Computational models of the spine have not been able to include accurate nonlinear and viscoelastic material properties, as they have not previously been measured. Capsules were tested using a uniaxial ramp-hold protocol or a haversine displacement protocol using a commercially available materials testing device. Plane strain was measured optically. Capsules were tested both parallel and perpendicular to the dominant orientation of the collagen fibers in the capsules. Viscoelastic material properties were determined. Parallel to the dominant orientation of the collagen fibers, the complex modulus of elasticity was E*=1.63MPa, with a storage modulus of E'=1.25MPa and a loss modulus of: E" =0.39MPa. The mean stress relaxation rates for static and dynamic loading were best fit with first-order polynomials: B(epsilon) = 0.1110epsilon-0.0733 and B(epsilon)= -0.1249epsilon + 0.0190, respectively. Perpendicular to the collagen fiber orientation, the viscous and elastic secant moduli were 1.81 and 1.00 MPa, respectively. The mean stress relaxation rate for static loading was best fit with a first-order polynomial: B (epsilon) = -0.04epsilon - 0.06. Capsule strength parallel and perpendicular to collagen fiber orientation was 1.90 and 0.95 MPa, respectively, and extensibility was 0.65 and 0.60, respectively. Poisson's ratio parallel and perpendicular to fiber orientation was 0.299 and 0.488, respectively. The elasticity moduli were nonlinear and anisotropic, and capsule strength was larger aligned parallel to the collagen fibers. The phase lag between stress and strain increased with haversine frequency, but the storage modulus remained large relative to the complex modulus. The stress relaxation rate was strain dependent parallel to the collagen fibers, but was strain independent perpendicularly.     

Elastic Behavior and Platelet Retraction in Low- and High-Density Fibrin?Gels

Fibrin is a biopolymer that gives thrombi the mechanical strength to withstand the forces imparted on them by blood flow. Importantly, fibrin is highly extensible, but strain hardens at low deformation rates. The density of fibrin in clots, especially arterial clots, is higher than that in gels made at plasma concentrations of fibrinogen (3–10 mg/mL), where most rheology studies have been conducted. Our objective in this study was to measure and characterize the elastic regimes of low (3–10 mg/mL) and high (30–100 mg/mL) density fibrin gels using shear and extensional rheology. Confocal microscopy of the gels shows that fiber density increases with fibrinogen concentration. At low strains, fibrin gels act as thermal networks independent of fibrinogen concentration. Within the low-strain regime, one can predict the mesh size of fibrin gels by the elastic modulus using semiflexible polymer theory. Significantly, this provides a link between gel mechanics and interstitial fluid flow. At moderate strains, we find that low-density fibrin gels act as nonaffine mechanical networks and transition to affine mechanical networks with increasing strains within the moderate regime, whereas high-density fibrin gels only act as affine mechanical networks. At high strains, the backbone of individual fibrin fibers stretches for all fibrin gels. Platelets can retract low-density gels by >80% of their initial volumes, but retraction is attenuated in high-density fibrin gels and with decreasing platelet density. Taken together, these results show that the nature of fibrin deformation is a strong function of fibrin fiber density, which has ramifications for the growth, embolization, and lysis of thrombi.     

Diffusing wave spectroscopy microrheology of actin filament networks.

Filamentous actin (F-actin), one of the constituents of the cytoskeleton, is believed to be the most important participant in the motion and mechanical integrity of eukaryotic cells. Traditionally, the viscoelastic moduli of F-actin networks have been measured by imposing a small mechanical strain and quantifying the resulting stress. The magnitude of the viscoelastic moduli, their concentration dependence and strain dependence, as well as the viscoelastic nature (solid-like or liquid-like) of networks of uncross-linked F-actin, have been the subjects of debate. Although this paper helps to resolve the debate and establishes the extent of the linear regime of F-actin networks' rheology, we report novel measurements of the high-frequency behavior of networks of F-actin, using a noninvasive light-scattering based technique, diffusing wave spectroscopy (DWS). Because no external strain is applied, our optical assay generates measurements of the mechanical properties of F-actin networks that avoid many ambiguities inherent in mechanical measurements. We observe that the elastic modulus has a small magnitude, no strain dependence, and a weak concentration dependence. Therefore, F-actin alone is not sufficient to generate the elastic modulus necessary to sustain the structural rigidity of most cells or support new cellular protrusions. Unlike previous studies, our measurements show that the mechanical properties of F-actin are highly dependent on the frequency content of the deformation. We show that the loss modulus unexpectedly dominates the elastic modulus at high frequencies, which are key for fast transitions. Finally, the measured mean square displacement of the optical probes, which is also generated by DWS measurements, offers new insight into the local bending fluctuations of the individual actin filaments and shows how they generate enhanced dissipation at short time scales.     

A constitutive model for the time-dependent,nonlinear stress response of fibrin networks

Blood clot formation is important to prevent blood loss in case of a vascular injury but disastrous when it occludes the vessel. As the mechanical properties of the clot are reported to be related to many diseases, it is important to have a good understanding of their characteristics. In this study, a constitutive model is presented that describes the nonlinear viscoelastic properties of the fibrin network, the main structural component of blood clots. The model is developed using results of experiments in which the fibrin network is subjected to a large amplitude oscillatory shear (LAOS) deformation. The results show three dominating nonlinear features: softening over multiple deformation cycles, strain stiffening and increasing viscous dissipation during a deformation cycle. These features are incorporated in a constitutive model based on the Kelvin–Voigt model. A network state parameter is introduced that takes into account the influence of the deformation history of the network. Furthermore, in the period following the LAOS deformation, the stiffness of the networks increases which is also incorporated in the model. The influence of cross-links created by factor XIII is investigated by comparing fibrin networks that have polymerized for 1 and 2 h. A sensitivity analysis provides insights into the influence of the eight fit parameters. The model developed is able to describe the rich, time-dependent, nonlinear behavior of the fibrin network. The model is relatively simple which makes it suitable for computational simulations of blood clot formation and is general enough to be used for other materials showing similar behavior.     

Nonlinear tensile properties of bovine articular cartilage and their variation with age and depth

Tensile stiffness of articular cartilage is much greater than its compressive stiffness and plays an essential role even in compressive properties by increasing transient fluid pressures during physiological loading. Recent studies of nonlinear properties of articular cartilage in compression revealed several physiologically pertinent nonlinear behaviors, all of which required that cartilage tensile stiffness increase significantly with stretch. We therefore performed sequences of uniaxial tension tests on fresh bovine articular cartilage slices using a protocol that allowed several hours to attain equilibrium and measured longitudinal and transverse tissue strain. By testing bovine cartilage from different ages (6 months to 6 years) we found that equilibrium and transient tensile modulus increased significantly with maturation and age, from 0 to 15 MPa at equilibrium and from 10 to 28 MPa transiently. Our results indicate that cartilage stiffens with age in a manner similar to other highly hydrated connective tissues, possibly due to age-dependent content of enzymatic and nonenzymatic collagen cross links. The long relaxation period used in our tests (5-10 hours) was necessary in order to attain equilibrium and avoid a very significant overestimation of equilibrium modulus that occurs when much shorter times are used (15-30 minutes). We also found that equilibrium and transient tensile modulus increased nonlinearly when cartilage is stretched from 0 to 10% strain without any previous tare load. Although our results estimate a nonlinear increase in tensile stiffness with stretch that is an order of magnitude lower than that required to predict nonlinear properties in compression, they are in agreement with previous results from other uniaxial tension tests of collagenous materials. We therefore speculate that biaxial tensile moduli may be much higher and thereby more compatible with observed nonlinear compressive properties.     

Viscoelastic shear properties of the corneal stroma

The cornea is a highly specialized transparent tissue which covers the front of the eye. It is a tough tissue responsible for refracting the light and protecting the sensitive internal contents of the eye. The biomechanical properties of the cornea are primarily derived from its extracellular matrix, the stroma. The majority of previous studies have used strip tensile and pressure inflation testing methods to determine material parameters of the corneal stroma. Since these techniques do not allow measurements of the shear properties, there is little information available on transverse shear modulus of the cornea. The primary objectives of the present study were to determine the viscoelastic behavior of the corneal stroma in shear and to investigate the effects of the compressive strain. A thorough knowledge of the shear properties is required for developing better material models for corneal biomechanics. In the present study, torsional shear experiments were conducted at different levels of compressive strain (0–30%) on porcine corneal buttons. First, the range of linear viscoelasticity was determined from strain sweep experiments. Then, frequency sweep experiments with a shear strain amplitude of 0.2% (which was within the region of linear viscoelasticity) were performed. The corneal stroma exhibited viscoelastic properties in shear. The shear storage modulus, G′, and shear loss modulus, G″, were reported as a function of tissue compression. It was found that although both of these parameters were dependent on frequency, shear strain amplitude, and compressive strain, the average shear storage and loss moduli varied from 2 to 8 kPa, and 0.3 to 1.2 kPa, respectively. Therefore, it can be concluded that the transverse shear modulus is of the same order of magnitude as the out-of-plane Young's modulus and is about three orders of magnitude lower than the in-plane Young's modulus.     

Elastic moduli, yield stress, and ultimate stress of cancellous bone in the canine proximal femur

Elastic moduli, yield stress and ultimate compressive stress were determined for cancellous bone from the femoral head and neck regions of the canine femur. Unconfined compression tests were performed on 5 mm cubic samples which were cut from two femurs. Elastic moduli were measured in three orthogonal directions, and the yield stress and ultimate stress were measured along the proximal-distal axis. The results from this investigation support previous assumptions that the mechanical behavior of canine cancellous bone is qualitatively similar to human cancellous bone. The canine cancellous bone was observed to be anisotropic in elastic modulus. For two thirds of the cubic specimens tested, the elastic modulus was largest in the load-bearing, proximal-distal direction. A linear relationship between yield stress and elastic modulus was observed for canine bone, as is typical of human bone. A similar linear relationship between ultimate stress and elastic modulus was observed. Thus, for canine bone as well as for human bone, failure appears to be governed by a strain level which is position independent. The yield strain of 0.0259 and ultimate strain of 0.0288 for canine bone were both less than the yield strain of 0.0395 reported for human bone.     

股骨头负重区松质骨的压缩力学特性

本文对19具新鲜青年(30左右)尸体股骨负重区的松质骨进行了压缩测试,测算并提供了一组松质骨弹性模量,极限应力,应变,屈服载荷及能量吸收值。试验表明松质骨力学性能主要缓解外力冲击加压。     

Load transmission in the nasofrontal suture of the pig, Sus scrofa

The nasofrontal suture links the nasal complex with the braincase and is subject to compressive strain during mastication and (theoretically) tensile strain during growth of nasal soft tissues. The suture's ability to transmit compressive and tensile loads therefore affects both cranioskeletal stress distribution and growth. This study investigated the in vitro viscoelastic and failure properties of the nasofrontal suture in the pig, Sus scrofa. Suture specimens from two ages were tested in compression and tension and at fast and slow rates. In additional specimens, strain gauges were applied to the suture and nasal bone for strain measurement during testing. Relaxation testing demonstrated higher elastic moduli in tension than compression, regardless of test rate or pig age. In contrast, maximum elastic moduli from failure tests, as well as peak stresses, were significantly higher in compression than in tension. Sutures from older pigs tended to have higher elastic moduli and peak stresses, significantly so for tensile relaxation moduli. Strain gauge results showed that deformation at the suture was much greater than that of the nasal bone. These data demonstrate the viscoelasticity and deformability of the nasofrontal sutural ligament. The suture achieved maximal resistance to tensile deformation at low loads, corresponding with the low tensile loads likely to occur during growth of nasal soft tissues. In contrast, the maximal stiffness in compression at high loads indicates that the suture functions with a substantial safety factor during mastication.     

Micro- and macrorheological properties of actin networks effectively cross-linked by depletion forces

The structure and rheology of cytoskeletal networks are regulated by actin binding proteins. Aside from these specific interactions, depletion forces can also alter the properties of cytoskeletal networks. Here we demonstrate that the addition of poly(ethylene glycol) (PEG) as a depletion agent results not only in severe structural changes, but also in alterations in mechanical properties of actin solutions. In the plateau of the elastic modulus two regimes can be distinguished by micro and macrorheological methods. In the first, the elastic modulus increases only slightly with increasing depletion agent, whereas above a critical concentration c*, a strong increase of cPEG6k3.5 is observed in a distinct second regime. Microrheological data and electron microscopy images show a homogenous network of actin filaments in the first regime, whereas at higher PEG concentrations a network of actin bundles is observed. The concentration dependence of the plateau modulus G0, the shift in entanglement time taue, and the nonlinear response indicate that below c* the network becomes effectively cross-linked, whereas above c* G0(cPEG6k) is primarily determined by the network of bundles that exhibits a linearly increasing bundle thickness.     

Effects of oxidative stress-induced changes in the actin cytoskeletal structure on myoblast damage under compressive stress: confocal-based cell-specific finite element analysis

Muscle cells are frequently subjected to both mechanical and oxidative stresses in various physiological and pathological situations. To explore the mechanical mechanism of muscle cell damage under loading and oxidative stresses, we experimentally studied the effects of extrinsic hydrogen peroxides on the actin cytoskeletal structure in C2C12 myoblasts and presented a finite element (FE) analysis of how such changes in the actin cytoskeletal structure affected a myoblast’s capability to resist damage under compression. A confocal-based cell-specific FE model was built to parametrically study the effects of stress fiber density, fiber cross-sectional area, fiber tensile prestrain, as well as the elastic moduli of the stress fibers, actin cortex, nucleus and cytoplasm. The results showed that a decrease in the elastic moduli of both the stress fibers and actin cortex could increase the average tensile strain on the actin cortex–membrane structure and reduce the apparent cell elastic modulus. Assuming the cell would die when a certain percentage of membrane elements were strained beyond a threshold, a lower elastic modulus of actin cytoskeleton would compromise the compressive resistance of a myoblast and lead to cell death more readily. This model was used with a Weibull distribution function to successfully describe the extent of myoblasts damaged in a monolayer under compression.     

Metabolic network alignment in large scale by network compression

Metabolic network alignment is a system scale comparative analysis that discovers important similarities and differences across different metabolisms and organisms. Although the problem of aligning metabolic networks has been considered in the past, the computational complexity of the existing solutions has so far limited their use to moderately sized networks. In this paper, we address the problem of aligning two metabolic networks, particularly when both of them are too large to be dealt with using existing methods. We develop a generic framework that can significantly improve the scale of the networks that can be aligned in practical time. Our framework has three major phases, namely the compression phase, the alignment phase and the refinement phase. For the first phase, we develop an algorithm which transforms the given networks to a compressed domain where they are summarized using fewer nodes, termed supernodes, and interactions. In the second phase, we carry out the alignment in the compressed domain using an existing network alignment method as our base algorithm. This alignment results in supernode mappings in the compressed domain, each of which are smaller instances of network alignment problem. In the third phase, we solve each of the instances using the base alignment algorithm to refine the alignment results. We provide a user defined parameter to control the number of compression levels which generally determines the tradeoff between the quality of the alignment versus how fast the algorithm runs. Our experiments on the networks from KEGG pathway database demonstrate that the compression method we propose reduces the sizes of metabolic networks by almost half at each compression level which provides an expected speedup of more than an order of magnitude. We also observe that the alignments obtained by only one level of compression capture the original alignment results with high accuracy. Together, these suggest that our framework results in alignments that are comparable to existing algorithms and can do this with practical resource utilization for large scale networks that existing algorithms could not handle. As an example of our method's performance in practice, the alignment of organism-wide metabolic networks of human (1615 reactions) and mouse (1600 reactions) was performed under three minutes by only using a single level of compression.     

Phase equilibria and gelation in gelatin/maltodextrin systems — Part IV: composition-dependence of mixed-gel moduli

The storage moduli (G′) of phase-separated co-gels formed by quench-cooling mixed solutions of gelatin and potato maltodextrin (Paselli SA-2 and SA-6) have been related quantitatively to the experimentally-determined concentration-dependence of G′ for the constituent polymers. Distribution of water between the phases was examined explicitly by using polymer blending laws to derive calculated moduli for gelatin-continuous and maltodextrin-continuous networks over the entire range of solvent partition. Allowance was made for the direct contribution of polymer chains, and for density differences between the phases, in calculating relative phase-volumes. The effect of gel formation prior to phase-separation was calculated using classical theory for network de-swelling. Good agreement with observed moduli for more than 30 gelatin/maltodextrin combinations was achieved using a single adjustable parameter, p (the ratio of solvent to polymer in the gelatin phase divided by the same ratio for the maltodextrin phase), with an optimum value of p ≈ 1·8 for both SA-6 and SA-2.     

Rheological properties of cysteine-containing elastin-like polypeptide solutions and hydrogels

The rheological properties of cysteine-containing elastin-like polypeptide (Cys-ELP) solutions and Cys-ELP hydrogels are reported. The Cys-ELP solutions exhibit a surprisingly high apparent viscosity at low shear rate. The high viscosity is attributed to the formation of an interfacial cross-linked "skin" at the sample surface, rather than the bulk of the Cys-ELP solution. At higher shear rate, the interfacial cross-linked film breaks, and its influence on the viscosity of the Cys-ELP solution can be ignored. Cys-ELP hydrogels are formed by mixing Cys-ELP and hydrogen peroxide (H(2)O(2)). At fixed concentration of Cys-ELP, the gelation time can be tuned by the concentration of H(2)O(2). Cys-ELP hydrogels have the typical characteristics of covalent cross-linked networks, as the storage moduli are larger than the loss moduli and are independent of frequency in dynamic oscillatory frequency sweep experiments. The plateau moduli obtained from linear frequency sweep experiments are much lower than those estimated from the number of thiol groups along the Cys-ELP chain, indicating that only a small fraction of thiols form elastically active cross-links. From the small value of the fraction of elastically active cross-links, the Cys-ELP hydrogel is concluded to be an inhomogenous network. Under steady shear, a 2.5 wt % Cys-ELP hydrogel shear thickens at shear rates lower than that necessary for fracture.