Nonlinear Viscoelasticity of Concentrated Solutions of Aggrecan

Biomacromolecules 2001, 2, 780-787

780

Nonlinear Viscoelasticity of Concentrated Solutions of Aggrecan Aggregate Nispa Meechai, Alexander M. Jamieson, John Blackwell, and David A. Carrino* Departments of Macromolecular Science and Biology, Case Western Reserve University, Cleveland, Ohio 44106

Rekha Bansal Gliatech Corporation, Beachwood, Ohio Received February 13, 2001; Revised Manuscript Received May 24, 2001

Aggrecan, the major cartilage proteoglycan, is the macromolecular species primarily involved in the resiliency of cartilage tissue. Most aggrecan molecules occur in cartilage extracellular matrix as aggregates. Each aggregate has a supramolecular structure, with many highly anionic, brushlike aggrecan subunits noncovalently bound to a hyaluronan chain. To better examine the viscoelastic properties of aggrecan aggregate, contaminating subunits were removed by exclusion chromatography. At physiologic ionic strength, concentrated solutions of purified aggrecan aggregate exhibit predominantly elastic behavior at small shear strains. However, above a critical strain, γc, the shear moduli show a pronounced strain-softening transition, where the storage modulus decreases suddenly, and the loss modulus exhibits a maximum. At small stresses, the creep function is also highly elastic, exhibiting an equilibrium compliance and large recoverable compliance. When the stress is amplified, a discrete transition to viscous flow occurs at a yield stress σy. These nonlinear responses are similar to previous observations for close-packed colloidal suspensions of soft spheres, such as microgel or emulsion particles, for which a yield transition occurs when the stress and deformation are sufficient to move a particle past its neighbors. Introduction Normal articular cartilage is an avascular tissue in which chondrocytes are sparsely distributed in an extracellular matrix, whose major role is to act as a load-bearing structure to protect the joint from excessive mechanical stresses. The physical properties of cartilage are determined by the extracellular matrix, which is a porous network of insoluble collagen fibers permeated by a concentrated solution of proteoglycan (aggrecan) aggregate (PGA).1 Each aggregate is a supramolecular structure, in which up to 100 aggrecan subunit molecules are bound through noncovalent interactions to a hyaluronan chain. The aggrecan subunit has a polyelectrolyte brush structure consisting of a protein backbone with pendant glycosaminoglycan chains, specifically chondroitin sulfate and keratan sulfate, covalently bound to serine or threonine residues of the protein backbone. The glycosaminoglycan side chains contain negatively charged carboxylate and sulfate groups, whose electrostatic repulsions cause aggrecan subunits to assume a stiff extended conformation. In the native tissue, the binding between subunits and hyaluronan is stabilized by a third macromolecular species referred to as link protein.2 Aggregates are thus exceptionally large entities, with molecular weights ranging up to a hundred million. The ratio of aggregate to subunit depends on cartilage type, age, and disease.3,4 The formation of aggregate promotes immobilization of aggrecan within the collagen network and contributes to the compressive rigidity of the

extracellular matrix,4-7 over 90% of which, under dynamic loading conditions, is generated by interstitial fluid pressure.8 Viscoelastic behavior of concentrated solutions of aggrecan aggregate has been studied by several groups in the linear viscoelastic regime, i.e., at applied stresses sufficiently small that the strains are proportional to the stresses.9,10-14 Significant differences were observed between the properties of different aggrecan aggregate preparations. For example, Mow et al. (1984) reported primarily viscous behavior (tan δ >1), whereas predominantly elastic responses were observed by other investigators at comparable or lower concentrations.10,12,14 Such discrepancies are presumed to be the result of variations in the structure of different specimens. For example, aggregate preparations are generally a mixture of aggregate and subunit, and it is known that the rheological properties are influenced by the proportion of aggrecan present as aggregate (percent aggregation).9,12 The rheological properties of concentrated solutions of subunit exhibit primarily viscous behavior.10,12,14 Noting that the dynamic modulus of concentrated solutions of aggrecan aggregate is only ∼ 1 Pa, whereas the dynamic modulus of cartilage is ∼1 × 106 Pa, Hardingham et al. suggest that the function of aggrecan is not to provide shear stiffness, but to control the spatial organization of the collagen fibrils.15 The focus of the present study is to investigate the nonlinear viscoelastic properties of concentrated solutions of aggrecan aggregate, with the aim of gaining insight into the molecular origin of the elasticity of concentrated solutions

10.1021/bm015520g CCC: $20.00 © 2001 American Chemical Society Published on Web 07/28/2001

Biomacromolecules, Vol. 2, No. 3, 2001 781

Solutions of Aggrecan Aggregate

Table 1. Physical Properties of Aggrecan Materials in 0.15 M NaCl, 0.01 M Tris Buffer, pH 6.8 PGA

Mw × 10-6

Rg (nm)

Rh (nm)

Rg/Rh

C*(Rh) (mg/mL)

Mn × 10-6

% aggregate

L-PGA 54 L-PGA 80 S-PGA 75 100% L-PGA 54 100% L-PGA 80 aggrecan subunit

38.0 ( 2.65 43.0 ( 2.12 18 9.6 ( 0.40 15.3 ( 1.53 2.93

337 ( 29 285 ( 21 212 120 ( 8.7 166 ( 8.5 94

295 210 148 95 ( 5 105 ( 7 60

1.14 1.36 1.43 1.26 1.58 1.57

0.59 1.84 2.20 4.44 5.24 5.38

6 12 8

54 80 75 100 100

of these molecules. Thus, we report the first studies of the creep response of concentrated solutions of aggrecan aggregate, which provides more definitive information on whether the material behaves as a viscoelastic solid or a viscoelastic fluid at very low levels of applied shear. We also investigate the strain dependence of the storage and loss moduli. The influence of aggregate/subunit ratio and of aggregate size on the viscoelastic behavior is explored. The experimental observations are discussed in comparison to the known properties of concentrated suspensions of soft spheroids. Materials and Methods (a) Isolation and Purification of Aggrecan-A1 from Bovine Nasal Septum. The rheological behavior of several different aggrecan aggregate preparations was investigated in this study. Each specimen was extracted from a different source of bovine nasal septum as an A1 preparation as follows.16 (i) Guanidine Hydrochloride (GdnHCl) Extraction. Cartilage from bovine nasal septum (Pel-Freeze Biologicals, Rogers, AR) was minced into small pieces and stirred overnight in extraction buffer (4 M GdnHCl containing benzamidine hydrochloride, phenylmethylsulfonyl fluoride, N-ethylmaleimide, ethylenediamine tetraacetate, 6-aminocaproic acid, and sodium acetate, pH 5.8). The filtered extract was dialyzed at 4°C to 0.4 M GdnHCl, containing the same additives as the extraction buffer. (ii) Density Gradient Centrifugation. To the above solution was added solid cesium chloride to a final density of 1.499 g/mL for a specimen designated as L-PGA54 and to 1.65 g/mL for specimens designated as L-PGA80 and S-PGA75. The resulting solution was then ultracentrifuged in a 50Ti rotor (Beckman Instruments) at 35 000 rpm for 45 h at 10°C. The gradient was cut into four approximately equal fractions (A1-A4), and the density of each fraction was measured. Results showed that the majority of aggrecan aggregate was recovered in the bottom (A1) fraction. The A1 fraction was dialyzed against water at 4°C and lyophilized. (B) Determination of Percent Aggregate. Aggrecan aggregate, dissolved in 0.4 M GdnHCl, 0.05 M sodium acetate, pH 7, was subjected to gel exclusion chromatography through a Sepharose CL-2B column eluted with the same solution used to dissolve the sample. Aliquots of each column fraction were assayed by a dye-binding assay with the cationic dye Safranin O, which binds to and precipitates glycosaminoglycans.17 The Safranin O-aggrecan precipitates were collected on a nitrocellulose membrane with a dot-blot

Figure 1. Gel permeation chromatograph of aggrecan aggregate on Sepharose CL-2B column with 0.4 M GdnHCl, 0.05 M sodium acetate, pH 7, as eluent.

apparatus. The dye from the precipitates, which is proportional to the amount of aggrecan, was extracted with 10% cetylpyridinium chloride, and the absorbance for each fraction was measured in a Shimadzu UV 160 spectrophotometer at 536 nm to produce the chromatogram shown in Figure 1. The first peak represents the fractions eluted in the column void volume, which is the position at which aggregate molecules elute from the column. Because of their smaller hydrodynamic volume, subunit molecules elute later. The fraction of the total area which elutes in the void volume is reported as the percent aggregate in Table 1. (c) Light-Scattering Measurements. Light-scattering experiments were performed on a Brookhaven Instrument (BI) Corporation spectrometer with a Spectra Physics 15 mW He/Ne laser (λ ) 632.8 nm). All measurements were made at 25 °C. Absolute calibration of the spectrometer was made with double-distilled toluene, using the Rayleigh ratio for vertically polarized light Rv ) 14 × 10-6 cm-1.18 Weightaverage molecular weight (Mw) and radius of gyration (Rg) of aggregate samples in 0.15 M NaCl, 0.01 M tris(hydroxymethyl)aminomethane (Tris), pH 6.8, were obtained from intensity measurements carried out at scattering angles in the range 30-90°. (dnj/dc)µs for aggrecan solutions in 0.15 M NaCl, 0.01 M Tris, pH 6.8, is 0.15 mL/g.19,20 Dynamic light-scattering measurements on aggrecan solutions in 0.15 M NaCl, 0.01 M Tris, pH 6.8, were performed at angles ranging from 25 to 40° with a 264-channel BI 2030 AT 4-bit correlator. The translational diffusion coefficient Dot,o was obtained by extrapolation to zero wave vector and concentration. The hydrodynamic radius (Rh) is calculated from the Stokes-Einstein equation, Rh ) kBT/(6πηsDot,o). Table 1 lists the corresponding values of molecular weight (Mw), radius of gyration (Rg), and hydrodynamic radius (Rh) of aggregate samples, as well as number-average molecular

782

Biomacromolecules, Vol. 2, No. 3, 2001

weight (Mn), estimated by combining the data on Mw and percent aggregate. Two samples were designated L-PGA because they have aggregates of large size, while the third, having aggregates of smaller size, was designated S-PGA. However, the use of a lower starting buoyant density for density gradient centrifugation of L-PGA54 leads to a lower proportion of aggregate (54 wt %) in this sample compared to the other two (80 wt % in L-PGA80 and 75 wt % in S-PGA75). The origin of the smaller Mw, Rg, and Rh values measured for the S-PGA sample is not known, but may reflect sample to sample variability. These distinct samples enable us to study the effect of aggregate size on the viscoelastic properties. (d) Preparation of Subunit-Free Aggregate. To investigate the influence of free aggrecan subunit on the viscoelastic properties of concentrated L-PGA solutions, two further L-PGA specimens were prepared, consisting only of aggregate molecules, which elute in the void volume of a Sepharose CL-2B column as described above. Aggregate fractions recovered at the column void volume were collected, pooled, dialyzed against water, and then lyophilized to dryness to obtain subunit-free aggregate specimens, which we designate 100% L-PGA54 and 100% L-PGA80. The Mw, Rg, and Rh values of the 100% L-PGA samples were found to be smaller than those of the unfractionated specimens (LPGA), as evident in Table 1. This may result from inefficient recovery of the largest molecules, as suggested by the fact that recovery of material from the column is in the range of 75%. Column fractionation separates aggrecan aggregate not only from aggrecan subunits but also from any other small proteins and nucleic acids, which may be present as contaminants. (e) Rheological Measurements. Aggrecan aggregate solutions at a concentration appropriate for rheological analysis were prepared by dissolving freeze-dried aggrecan aggregate in aqueous saline solution with occasional gentle shaking for at least 48 h at 4°C. The solutions were subsequently centrifuged at 2000 rpm for 10 min to remove air bubbles before performing the rheological experiments. A Carrimed 50 controlled stress rheometer was used to perform creep and creep recovery experiments. The testing geometry used was stainless steel parallel plates (40 mm diameter with 200 µm gap) with a solvent trap feature to prevent solvent evaporation during testing. Dynamic oscillatory experiments were performed with a Rheometrics Instruments controlled-strain rheometer, using a stainless steel cone and plate geometry (50 mm diameter with 0.02 rad cone angle) contained in a temperature-controlled chamber to maintain 100% humidity. All tests were performed at 25°C. Results and Discussion A. Viscoelastic Properties of Unfractionated Solutions of Large Aggrecan Aggregate. (i) Storage and Loss Modulus. The rheological behavior of the L-PGA54 and L-PGA80 samples was investigated at the same concentration (32 mg/mL) in aqueous 0.15 M NaCl, 0.01 M Tris, pH 6.8. Figure 2 shows values of the storage and loss moduli, G′-

Meechai et al.

Figure 2. Storage and loss moduli, G′(ω) and G′′(ω), dynamic viscosity, η*(ω), and tan δ for 32 mg/mL L-PGA54 (open symbols) and L-PGA80 (closed symbols) in 0.15 M NaCl, 0.15 M Tris, pH 6.8.

(ω) and G′′(ω), the dynamic viscosity, η*(ω), and tan δ ) G′′(ω)/G′(ω) determined via a dynamic frequency sweep at 10% strain performed from angular frequency ω ) 0.01100 rad/s. Despite having different aggrecan subunit contents, each L-PGA specimen exhibits a similar viscoelastic response, predominantly elastic at low frequency, which suggests the existence of a network structure. We ascribe the similarity between L-PGA54 and L-PGA80 to the fact that, as is evident in Table 1, L-PGA80 has a higher aggregate content but a smaller hydrodynamic volume. Thus, the overlap concentration, estimated as C* ) 3M/4πNARh3, is, in fact, smaller for L-PGA54 (C* ) 0.6 mg/mL) compared to L-PGA80 (C* ) 1.9 mg/mL). Hence, at 32 mg/mL and taking into account the fact that only 54% and 80% of the material is aggregate, C/C* ∼ 29 and 14 for L-PGA54 and L-PGA80, respectively. At a high frequency of deformation, the L-PGA solutions each show a crossover to a viscous response reflecting dissipative behavior of the remaining free aggregan subunits. The L-PGA solutions show weak nonlinearity such that the elasticity decreases slightly with increase of strain, as evident in Figure 3, which shows, for L-PGA54, a strain loop in the range from 1 to 100% strain for G′(ω), G′′(ω), and tan δ at a frequency ω ) 0.5 rad/s. With increase of strain, γ, the storage modulus decreases relative to the loss modulus, so that tan δ increases above unity, which is indicative of a more dissipative response, presumably due to disruption of the putative network. As evident in Figure 3, however, upon subsequent decrease of the strain, tan δ decreases below unity again, which suggests that the network structure reforms at small strains.21,22 However, the significant hysteresis between the upward and downward parts of the loop indicates that the network structure does not fully recover within the time scale of the loop (∼10 min). Weakly nonlinear behavior, essentially identical to that in Figure 3, was also observed for specimen L-PGA80 (not shown). Figure 4 shows a comparison of the dynamic shear viscosity, η*(ω), vs the steady-shear viscosity, η(γ˘ ), for 32 mg/mL L-PGA54 in aqueous 0.15 M NaCl, 0.01 M Tris, pH 6.8, at comparable angular frequency and shear rate. The L-PGA54 solution shows pronounced shear-thinning rheology at all frequencies and shear rates studied with a


Figure 3. (a,b) Storage and loss moduli, G′ and G′′, and tan δ, as a function of % strain at a frequency of 0.5 rad/s where closed symbols with line represent forward strain sweep (γ ) 1-100%) and open symbols represent backward sweep (γ ) 100-1%).

Figure 4. Dynamic and steady shear viscosities, η*(ω) and η(γ˘ ), and tan δ, as a function of frequency and shear rate for 32 mg/mL L-PGA54 in 0.15 M NaCl, 0.01 M Tris, pH 6.8

characteristic failure of the Cox-Merz relation at low ω and γ˘ , viz. η*(ω) > η(γ˘ ). Equivalent behavior was again observed for the corresponding L-PGA80 solution (not shown). Such failure is often observed for weak physical gels23 and is associated with a tendency to form network structures which are broken down under the applied strain. (ii) Creep Response. To gain further insight into the origin of the elastic response of the concentrated aggrecan aggregate solution, creep experiments were performed using the Carrimed controlled-stress rheometer. In Figure 5, parts a and b, the creep function of 32 mg/mL L-PGA54 solution is plotted as compliance, J(t) ) γ(t)/σ, vs time for increasing levels of applied stress, σ. At low stress (σ e 0.1 Pa), as seen in Figure 5a, the solution shows highly elastic behavior, as indicated by the appearance of an equilibrium compliance and large recoverable compliance. The equilibrium elastic


Figure 5. (a,b) Shear compliance, J(t), of 32 mg/mL L-PGA54 in 0.15 M NaCl, 0.01 M Tris, pH 6.8 at applied stress 0.1, 0.3, and 0.4 Pa.

modulus is estimated after 180 s from the equilibrium compliance to be Ge ) 1/Je ) 0.19 Pa. The corresponding value of Ge, estimated by linear extrapolation of the G′ measurement in Figure 2 to ω ) 0.001 rad/s, is 0.20 Pa, which indicates that the controlled stress and controlled strain measurements are self-consistent. When the applied stress is increased to 0.3 Pa, a transitional response is observed such that, initially, the material deforms elastically, as at lower stress, but then begins to flow after about 100 second (Figure 5a). This is an indication that the applied stress is close to the yield stress, σy. A similar transient creep response was previously reported for concentrated synthetic microgel particles24 and was interpreted on the basis of a lattice model of close-packed deformable spheres. Theoretical prediction for a lattice of monodisperse rigid spheres shows that a critical yield strain, γc, is 57%, while for deformable spheres, the critical strain is less.24,25 If deformable microgel particles are maintained under stress long enough near γc, water is slowly exuded from the microgel particles. When enough solvent is exuded, the gel particle can slip past its neighbors and flow occurs. From Figure 5a, the time scale for this process is τ ∼ 100 s. Following earlier analysis of macrogel behavior,26-29 Ketz et al. suggest the relationship τ ) ηa2/ Gkp, where ηs is the solvent viscosity, a the particle radius, G the modulus of the microgel, and kp the permeability of the particles.24 Using ηs ) 0.001 Pa‚s, a ) 300 nm, G ) 0.2 Pa, we determine kp ) 4.5 × 10-18 m2. The hydraulic permeability of cartilage is in the range (1-6) × 10-16 m2 s-1 Pa-1 as reported by Maroudas.30 Multiplication of this value by the viscosity of water, 0.001 Pa‚s, indicates kp ) (1-6) × 10-19 m2. Since the permeability of the aggrecan compartment decreases dramatically for a very small change

784


Figure 6. (a,b) Shear compliance, J(t), of 32 mg/mL L-PGA80 in 0.15 M NaCl, 0.01 M Tris, pH 6.8 at applied stress 0.1, 0.2, 0.25, and 0.3 Pa.

in aggrecan concentration,1 we infer that the lower permeability of cartilage results from the higher content of aggrecan (up to 50-80 mg/mL). In Figure 5a, it is further apparent that if the applied stress is removed quickly, the material is able to recover a considerable amount of strain, indicative of the material retaining a memory of the equilibrium network structure despite the substantial deformation. When the applied stress is further increased to 0.4 Pa, as seen in Figure 5b, the aggrecan aggregate solution yields and flows as a viscous fluid with a large permanent deformation, which increases with time. On removal of the stress, however, a significant recoverable compliance is still observed with magnitude comparable to that at 0.3 Pa, which again indicates that, despite the large deformation, interparticle and intraparticle forces drive restructuring of the equilibrium network structure. The creep response of L-PGA80 at 32 mg/mL, as shown in Figure 6, exhibits similar behavior to that of L-PGA54, elastic at small stress (σ < 0.1 Pa), except that L-PGA80 exhibits a small permanent set (∼20%). After t ∼ 100 second a distinct yield transition appears at σ ) 0.2 Pa, and more visibly at σ ) 0.25 Pa, and viscous flow occurs at σ ) 0.3 Pa. From Figure 6, we estimate a value of the steady-state compliance Jeo ∼ 5.5 Pa-1 which corresponds to a recovery modulus GR ) (Jeo)-1 ) 0.18 Pa, again numerically consistent with the value G′ ) 0.2 Pa, estimated by extrapolation to ω ) 0.001 rad/s in Figure 2. In addition to the above referenced behavior of concentrated microgel dispersions,24 similar creep characteristics to those in Figures 5 and 6 have been observed in concentrated charge-stabilized latex suspensions31 and in concentrated sterically stabilized silica particles dispersed in mineral oil21

Meechai et al.

at volume fractions, φ, near the maximum packing volume fraction, φm. Mechanistically, these observations can be interpreted in terms of a defect lattice model.31 At very low stress, an equilibrium compliance is observed with 100% recovery, indicative that the lattice is strong enough to resist flow at low stress, and hence the material acts as an elastic solid. As stress is increased, a more fluid response with some permanent set may be observed, which is interpreted as a “defect flow,” where the applied stress biases the interaction potential and the particles hop into vacant sites (defects) to release the strain. At yet higher stresses, sufficient to overcome the interparticle potential, viscous flow is observed.31 We accordingly propose that, at low stresses, concentrated solutions of aggrecan aggregate exhibit elastic solid behavior, with a recoverable compliance that depends on aggrecan aggregate concentration, particle size, and aggrecan subunit content, as well as the level of applied stress. In particular, for a given stress level, at lower packing densities, i.e., lower values of C/C*, “defect flow” may occur to produce some level of permanent set, as in L-PGA80. Finally, a transition to viscous flow is observed, at a critical yield stress, which also increases with C/C*, cf. σy ∼ 0.3 Pa for L-PGA54 and σy ∼ 0.2 Pa for L-PGA80. B. Viscoelastic Properties of Fractionated 100% L-PGA Solutions. The influence of aggrecan subunit content on the linear and nonlinear viscoelastic properties of concentrated solutions of aggrecan aggregate was investigated by comparing the behavior of the fractionated specimens (100% L-PGA) vs that of the unfractionated material (L-PGA). (i) Linear Viscoelastic Behavior. The storage and loss moduli, G′(ω) and G′′(ω), of l00% L-PGA54 at a concentration of 29 mg/mL and of 100% L-PGA80 at a concentration of 32 mg/mL in the angular frequency range from ω ) 0.01100 rad/s are shown in Figure 7, parts a and b, respectively. The results may be contrasted with the corresponding data for unfractionated L-PGA54 and unfractionated L-PGA80 (Figure 2). Evidently, all four samples exhibit a predominantly elastic response at low frequencies (tan δ ) G′′(ω)/ G′(ω) < 1), with a crossover to a viscous response at higher frequency. However, the fractionated materials have higher elasticity (i.e., smaller tan δ) at intermediate frequencies, 0.1 < ω < 10 rad/s. Also, the moduli of the fractionated specimens are smaller, so that we have to apply 10% strain to extend the measurements down to ω ) 0.01 rad/s (Figure 7). All of these differences are consistent with the fact that free aggrecan subunits are absent from the 100% L-PGA solution. Thus, in unfractionated L-PGA54, the dissipative response at all frequencies is enhanced by the presence of the unbound aggrecan subunit. Also, the magnitudes of G′ and G′′ at a specified frequency are scaled as the number of kinetically active units (G ∼ NpkT), which decreases substantially in the fractionated L-PGA solutions. We also note in Figure 7, parts a and b that a drop in G′ is observed at very low frequency, ω < 0.1 rad/s, indicative of the fact that the solutions of fractionated aggrecan aggregate can slowly relax on long time scales. (ii) Nonlinear Viscoelasticity. The strain dependence of G′ and G′′ for 100% L-PGA54 is exhibited in Figure 8. In contrast to the strain loop of the unfractionated L-PGA54



Figure 9. Dynamic loss modulus, G′′, as a function of % strain at three different deformation frequencies for 29 mg/mL L-PGA54 in 0.15 M NaCl, 0.01 M Tris, pH 6.8.

Figure 7. Storage and loss moduli, G′(ω) and G′′(ω), and dynamic viscosity, η*(ω) as a function of frequency at 5% (closed symbols) and 10% strain (open symbols) for (a) 29 mg/mL 100% L-PGA54 and (b) 32 mg/mL 100% L-PGA80, each dissolved in 0.15 M NaCl, 0.01 M Tris, pH 6.8.

Figure 8. Storage and loss moduli, G′(ω) and G, and tan δ as a function of % strain at frequency 0.5 rad/s for 29 mg/mL 100% L-PGA54 in 0.15 M NaCl, 0.01 M Tris, pH 6.8, where closed symbols with line represent the first forward strain sweep (1-100% γ), closed symbols without line represent backward strain sweep (100-1% γ) operated immediately after the first forward strain sweep is finished, and open symbols with line represent second forward strain sweep (1-100% γ) operated ∼30 min after the first strain loop.

solution shown in Figure 3, 100% L-PGA54 shows a pronounced nonlinearity, in the form of a precipitous decrease in G′ above a certain strain. In association with this, G′′ increases slightly to a maximum value at a strain level close to that where the viscoelastic response becomes primarily dissipative (tan δ ∼ 1). This behavior is very similar to a characteristic nonlinearity observed in the behavior of close-packed colloidal dispersions, when the applied strain becomes sufficient to cause particles to exchange positions with their neighbors.24,32-37 A decrease

in G′ and increase in G′′ occurs when the strain approaches a critical value where the particles are forced to exchange positions with their neighbors, and hence the material can more effectively dissipate the stress. Also shown in Figure 8, and consistent with the theoretical expectation discussed below, substantial recovery of the original elastic response is observed upon reversal of the strain sweep, although there is a significant hysteresis, which is likely due to a time lag between deformation and recovery of the aggregate hydrodynamic volume under shear. Indeed, also shown in Figure 8 is a second strain loop of the storage modulus, performed ∼30 min after the first, which shows that essentially complete recovery of the network elasticity has occurred. The above rheological observations on solutions of purified aggrecan aggregate, at concentrations considerably in excess of the overlap concentration, are qualitatively consistent with prediction of theoretical models for densely packed colloidal dispersions.32,36-38 In particular, we note the dynamic analysis of soft, glassy materials by Sollich,32 which predicts that, at small strains, γ, and low frequencies, ω, the rheological behavior is solidlike (G′ > G′′). At larger strains, a slight drop in G′ is observed, while G′′ increases slightly, which reflects the onset of nonlinear yielding and flow behavior. At the critical yield strain, γc, beyond which particles are forced to exchange positions with their neighbors, a strong nonlinearity is predicted such that a transition to a predominantly dissipative response is observed, G′ drops precipitously, G′′ exhibits a maximum, and G′′ > G′, which reflects the dominance of energy loss introduced by the nonlinear flow.36 Clearly, our observations (Figure 8) of the rheological behavior of concentrated solutions of subunit-free aggrecan aggregate are consistent with these predictions and indicate, for 29 mg/mL 100% L-PGA54, γc ∼ 30%. In addition, a further characteristic feature of the theoretical model is that the range of linear response is independent of the frequency of the applied strain.32 Our experiments indicate that, as shown in Figure 9 for 29 mg/mL 100% L-PGA54, the estimated maximum in G′′ is independent of frequency in the range 0.1 s-1 < ω < 10 s-1. To conclude this section, we show in Figure 10 that the creep response of 100% L-PGA80 at 32 mg/mL exhibits features similar to those of unfractionated L-PGA54 (Figure

786


Meechai et al.

Figure 11. Storage and loss moduli, G′(ω) and G′′(ω), dynamic and steady shear viscosities, η*(ω) and η(γ˘ ), for 60 mg/mL S-PGA75 in 0.15 M NaCl, 0.01 M Tris, pH 6.8.

Figure 10. a,b Shear compliance, J(t), of 32 mg/mL 100% L-PGA80 in 0.15 M NaCl, 0.01 M Tris, pH 6.8, at applied stresses of 0.1, 0.15, and 0.3 Pa.

5) and L-PGA80 (Figure 6), except that the yield point occurs at lower stresses. Thus, at σ ) 0.1 Pa, the solution exhibits the highly elastic “defect flow”, since the strains reached are considerably in excess of γc. There also appears to be some yield effect at this stress level after t ∼ 100 s. At σ ∼ 0.15 Pa, a distinct yield transition occurs, at σ ) 0.2 Pa, there still appears a yield effect (not shown), and at σ ) 0.3 Pa, viscous flow is observed, again with significant creep recovery on removal of stress. The observation that the yield stress range for 100% L-PGA80 appears smaller than for unfractionated L-PGA80 is consistent with the fact that the packing density, as indicated by C/C*, is smaller for 100% L-PGA80 (C/C* ∼ 4.9, cf. Table 1). The defect flow behavior of the creep response also agrees with the enhanced viscous behavior observed in the moduli at very low frequencies. Thus, in Figure 7, we have noted that it appears that a crossover may occur in G′ and G′′ below ω ) 0.01 rad/s, at a value we estimate at G′ ) G′′ ∼ 0.1 Pa. This is in reasonable agreement with the experimental value of the recoverable compliance, Jeo ∼ 12.5 Pa-1, obtained from the creep curve at the onset of yielding in Figure 10. C. Viscoelastic Behavior of S-PGA 75. Finally, in Figure 11, we present measurements of G′(ω) and G′′(ω) for the small aggrecan aggregate specimen, S-PGA75 in 0.15 M NaCl, 0.01 M Tris, pH 6.8 at an elevated aggrecan aggregate concentration of 60 mg/mL. Evidently, the viscoelastic properties of S-PGA75 are primarily viscous and therefore dramatically different from those of large aggrecan aggregate, L-PGA, as evident by comparison to Figure 2. We note that the overlap concentration for S-PGA, C* ) 2.2 mg/mL, and, thus, at 60 mg/mL, C/C* ∼ 21, which indicates that this concentration is considerably above the overlap concentra-

tion. This situation is consistent with our previous studies, which show that concentrated solutions of aggrecan subunit are viscous solutions, whereas solutions of large aggrecan aggregate at the same concentration are viscoelastic.12 These observations are again reminiscent of the rheological properties of concentrated colloidal dispersions, where it has been pointed out that, the smaller the disperse particle is, the more active is the Brownian motion and, consequently, the more difficult the formation of network structure.39 In this context, it is interesting to note that, despite having similar weightaverage molecular weight and particle size, the viscous character of concentrated S-PGA75 solutions is clearly different from that of solutions of subunit-free aggregate (100% L-PGA54 and 100% L-PGA80), which, as we have found, exhibit pronounced elastic properties. This contrasting behavior further illustrates the strong effect that the free subunit has on the viscoelastic properties. Concluding Remarks Our results indicate that, at high concentrations, aggrecan aggregate solutions exhibit viscoelastic properties characteristic of a transient network or a viscous solution, depending on the aggregate size and presence of free subunit. Aggrecan aggregate samples having hydrodynamic volumes large enough that Brownian motion cannot overcome the interparticle potential (L-PGA) show elastic behavior, which is enhanced if the sample has a low level of free subunit. The elasticity of concentrated aggrecan aggregate solutions also increases with packing density, as quantified by the reduced concentration C/C*. At small stresses, such solutions exhibit elastic solid or “defect flow” behavior, depending on the value of C/C*. When the applied stress or strain is increased above a certain value, σy and γc, the solutions exhibit a discrete yield transition to viscous flow. These rheological characteristics are very similar to those observed and predicted theoretically for concentrated suspensions of soft charged spheroids, such as microgel particles, emulsions, and ionically stabilized colloids. Such properties point to a further physiologic role of the aggrecan matrix. At small strains, the matrix behaves elastically, enabling it to stabilize the spatial organization of the collagen fibers. At large shear


strains, the matrix yields and recovers, allowing for pliancy of the connective tissue. References and Notes (1) Hascall, V. C. Biology of Carbohydrates; Ginsburg, V., Ed.; Wiley: New York, 1981; Vol. 1; p 1. (2) Tang, L. H.; Rosenberg, L.; Reihanian, H.; Jamieson, A. M.; Blackwell, J. Connect. Tissue Res. 1989, 19, 177. (3) Rosenberg, L. C.; Choi, H. U.; Tang, L. H.; Johnson, T. L.; Pal, S. J. Biol. Chem. 1985, 260, 6304. (4) Poole, A. R. Biochem. J. 1986, 236, 1. (5) Pottenger, L. A.; Lyon, N. B.; Hecht, J. D.; Neustadt, P. M.; Robinson, R. A. J. Biol. Chem. 1982, 257, 11479. (6) Muir, H. Biochem. Soc. Trans. 1983, 11, 613. (7) Ratcliffe, A.; Tyler, J.; Hardingham, T. E. Biochem. J. 1986, 238, 571. (8) Soltz, M. A.; Ateshian, G. A. Ann. Biomed. Eng. 2000, 28, 150. (9) Mow, V. C.; Mak, A. F.; Lai, W. M.; Rosenberg, L. C.; Tang, T. H. J. Biomech. 1984, 17, 325. (10) Matsumura, G. In Solution Properties of Polysaccharide Solutions; Brant, D. A., Ed.; American Chemical Society: Washington, DC, 1981; p 213. (11) Hardingham, T. E.; Muir, H.; Kwan, M. K.; Lai, W. M.; Mow, V. C. J. Orthop. Res. 1987, 5, 36. (12) Soby , L.; Jamieson, A. M.; Blackwell, J.; Choi, H. U.; Rosenberg, L. C. Biopolymers 1990, 29, 1587. (13) Zhu, W.; Lai, W. M.; Mow, M. C. J. Biomech. 1991, 24, 1007. (14) Tomika, M.; Matsumura, G. Carbohydr. Polym. 1995, 27, 197. (15) Hardingham, T. E.; Muir, H.; Kwan, M. K.; Lai, W. M.; Mow, V. C. J. Orthop. Res. 1987, 5, 36. (16) Hascall, V. C.; Kimura, J. H. Meth. Enzymol. 1982, 82, 769. (17) Carrino, D. A.; Arias, J. L.; Caplan, A. I. Biochem. Int. 1991, 24, 485.

Biomacromolecules, Vol. 2, No. 3, 2001 787 (18) Kaye, W.; McDaniel, J. B. Appl. Opt. 1974, 13, 1934. (19) Zangrando, D. D. Ph.D. Thesis, Case Western Reserve University, Cleveland, OH, 1990. (20) Li, X.; Reed, W. F. J. Chem. Phys. 1991, 94, 4568. (21) Jones, D. A. R.; Leary, B.; Boger, D. V. J. Colloid Interface Sci. 1991, 147, 479. (22) Yziquel, F.; Carreau, P. J.; Tanguy, P. A. Rheol. Acta 1999, 38, 14. (23) Ross-Murphy, S. B.; Shatwell, K. P. Biorheology 1993, 30, 217. (24) Ketz, R. J.; Prud’homme, R. K.; Graessley, W. W. Rheol. Acta 1988, 27, 531. (25) Pricen, H. M. J. Colloid Interface Sci. 1983, 91, 160. (26) Quinn T. M.; Grodzinsky, A. J. Macromolecules 1993, 26, 4332. (27) Mow, V. C.; Kuei, S. C.; Lai, W. M.; Armstrong, C. G. J. Biomech. Eng. 1980, 102, 73. (28) Frank, E. H.; Grodzinsky, A. J. J. Biomech. 1987, 20, 615-627. (29) Tanaka, T.; Hocker, L. O.; Benedek, G. B. J. Chem. Phys. 1973, 59, 5151. (30) Maroudas, A. The Joints and SynoVial Fluid; Sokoloff, L., Ed.; Academic Press: Orlando, FL, 1980; Vol 2; p 239. (31) Chen, L. B.; Zukoski, C. F. J. Chem. Soc., Faraday Trans. 1990, 86, 2629. (32) Sollich, P. Phys. ReV. E. 1998, 58, 738. (33) Frith, W. J.; Strivens, T. A.; Mewis, J. J. Colloid Interface Sci. 1990, 139, 55. (34) Mason, T. G.; Weitz, D. A. Phys. ReV. Lett. 1995, 75, 2770. (35) Mason, T. G.; Bibette, J.; Weitz, D. A. J. Colloid Interface Sci. 1996, 179, 439. (36) Mason, T. G.; Lacasse, M.-D.; Grest, G. S.; Levine, D.; Bibette. J.; Weitz, D. A. Phys. ReV. E. 1997, 56, 3150. (37) Kulicke, W. M.; Arendt, O.; Berger, M. Colloid Polym. Sci. 1998, 276, 1024. (38) Kraynick, A. M.; Hansen, M. G. J. Rheol. 1987, 31, 175. (39) Inoue, H.; Matsumoto, T. Colloid Surf. A 1996, 109, 89.

BM015520G

Nonlinear Viscoelasticity of Concentrated Solutions of Aggrecan

Recommend Documents