A MOLECULAR-MODEL OF PROTEOGLYCAN-ASSOCIATED ELECTROSTATIC FORCES IN CARTILAGE MECHANICS

Measured values of the swelling pressure of charged proteoglycans (PG) in solution (Williams RPW, and Comper WD; Biophysical Chemistry 36:22 3, 1990) and the ionic strength dependence of the equilibrium modulus of PG-rich articular cartilage (Eisenberg SR, and Grodzinsky AJ; J Ort hop Res 3: 148, 1985) are compared to the predictions of two models. E ach model is a representation of electrostatic forces arising from cha rge present on spatially fixed macromolecules and spatially mobile mic ro-ions. The first is a macroscopic continuum model based an Donnan eq uilibrium that includes no molecular-level structure and assumes that the electrical potential is spatially invariant within the polyelectro lyte medium (i.e. zero electric field). The second model is based on a microstructural, molecular-level solution of the Poisson-Boltzmann (P B) equation within a unit cell containing a charged glycosaminoglycan (GAG) molecule and its surrounding atmosphere of mobile ions. This lat ter approach accounts for the space-varying electrical potential and e lectrical field between the GAG constituents of the PG. In computation s involving no adjustable parameters, the PB-cell model agrees with th e measured pressure of PG solutions to within experimental error (10%) , whereas the ideal Donnan model overestimates the pressure by up to 3 -fold. In computations involving one adjustable parameter for each mod el, the PB-cell model predicts the ionic strength dependence of the eq uilibrium modulus of articular cartilage. Near physiological ionic str ength the Donnan model overpredicts the modulus data by 2-fold, but th e two models coincide for low ionic strengths (C-0 < 0.025M) where the spatially invariant Donnan potential is a closer approximation to the PB potential distribution. The PB-cell model result indicates that el ectrostatic forces between adjacent GAGs predominate in determining th e swelling pressure of PG in the concentration range found in articula r cartilage (20-80 mg/ml). The PB-cell model is also consistent with d ata (Eisenberg and Grodzinsky, 1985, Lai WM, Hou JS, and Mow VC; J Bio mech Eng 113: 245, 1991) showing that these electrostatic forces accou nt for similar to 1/2 (290kPa) the equilibrium modulus of cartilage at physiological ionic strength while absolute swelling pressures may be as low as similar to 25 - 100kPa. This important property of electros tatic repulsion between GAGs that are highly charged but spaced a few Debye lengths apart allows cartilage to resist compression (high modul us) without generating excessive intratissue swelling pressures