The density and strength of proteoglycan-proteoglycan interaction sites in concentrated solutions

Rheological flow properties of link-stable and link-free proteoglycan (PG) aggregates in concentrated solutions were measured using a cone-on-plate viscometer. A second-order constitutive model, based upon the statistical-network theories of Lodge, [Rheol. Acta 7, 379-392 (1968)] and De Kee and Carreau [J. Non-Newtonian Fluid Mech. 6, 127-143 (1979)], was developed to describe the measured steady and transient flow responses exhibited by the PG solutions. Our measurements confirmed previous experimental findings that the complex shear modulus of PG solutions depends on the frequency of the imposed small-amplitude oscillatory shear, and the apparent viscosity and primary normal-stress difference depend nonlinearly on the shear rate under steady-shear flow conditions [Mow et al., J. Biomechanics 17, 325-338 (1984b); Hardingham et al., J. orthop. Res. 5, 36-46 (1987)]. In the present study, we found that PG solutions exhibit pronounced stress overshoot responses and large hysteresis loop effects. These transient responses were shown to be sensitive to acceleration strain (i.e. the second rate of strain) as well as PG structure (i.e. link-protein stabilization). The model parameters were determined by curvefitting of the second-order constitutive model and experimental data from steady, oscillatory and transient shear flow measurements. Using this network model, we calculated the density of the idealized interaction sites existing in the PG network, and the average strength of these interaction sites. The results indicate that link-protein stabilization of PG aggregates does not change the density of interaction sites formed in the PG network, rather, it increases the average strength of these interaction sites.