The osmotic pressure of chondroitin sulfate (CS) solution in contact with an aqueous 1:1 salt reservoir of fixed ionic strength is studied using a recently developed coarse-grained molecular model. The effects of sulfation type (4- vs. 6-sulfation), sulfation pattern (statistical distribution of sulfate groups along a chain), ionic strength, CS intrinsic stiffness, and steric interactions on CS osmotic pressure are investigated. At physiological ionic strength (0.15 M NaCl), the sulfation type and pattern, as measured by a standard statistical description of copolymerization, are found to have a negligible influence on CS osmotic pressure, which depends principally on the mean volumetric fixed charge density. The intrinsic backbone stiffness characteristic of polysaccharides such as CS, however, is demonstrated to contribute significantly to its osmotic pressure behavior, which is similar to that of a solution of charged rods for the 20-disaccharide chains considered. Steric excluded volume is found to play a negligible role in determining CS osmotic pressure at physiological ionic strength due to the dominance of repulsive intermolecular electrostatic interactions that maintain chains maximally spaced in that regime, whereas at high ionic-strength steric interactions become dominant due to electrostatic screening. Osmotic pressure predictions are compared to experimental data and to well-established theoretical models including the Donnan theory and the Poisson-Boltzmann cylindrical cell model.
Articular cartilage is an avascular tissue that provides a low-friction, protective lining to the ends of contacting bones during joint locomotion. The tissue consists of a dense extracellular matrix of aggrecan and type II collagen that is maintained by a sparse volume fraction (~2%) of cells. Aggrecan is a high-molecular-weight proteoglycan (1-3.5 MDa) that consists of a linear protein backbone (~300 [Angstrom] contour length) with ~100 covalently bound anionic chondroitin sulfate (CS) glycosaminoglycans (GAGs), as well as a smaller molecular-weight fraction of keratin sulfate GAGs and other oligosaccharides (Fig. 1) (1,2). With the aid of link protein, aggrecan associates noncovalently with high-molecular-weight hyaluronic acid to form supramolecular complexes, helping to retain it in the extracellular matrix. The high negative charge density presented by the CS chains on aggrecan generates an osmotic swelling pressure that maintains articular cartilage in a hydrated state (60-80% water by weight) even under substantial compressive loads, and plays a central role in determining its compressive mechanical properties (3,4).

The CS constituent of aggrecan varies in chemical composition depending on the state of health or disease of articular cartilage (osteoarthritis or rheumatoid arthritis), anatomical site, depth within the cartilage layer, and age of the organism (5-12). For example, the fraction of 6-sulfated CS disaccharides in human femoral condyle cartilage increases with age from ~0.5 to 0.8 from birth to the age of 20 years with a concomitant decrease in 4-sulfation, after which it plateaus. Additionally, the concentration of 6-sulfated CS disaccharides in knee synovial fluid has been observed to be significantly lower in rheumatoid arthritis and osteoarthritis than in healthy tissue (10) and the concentration of 4-sulfated CS disaccharides higher in osteoarthritic hip cartilage, with only slight changes in overall GAG content (13). Considering the important role that CS plays in determining the mechanical properties of articular cartilage and these observed variations in CS chemical composition, it is of significant biological interest to understand the connection between CS composition and its osmotic pressure and conformation in detail. It is also of primary interest to gain a comprehensive understanding of the molecular origin of the mechanical properties of GAGs and proteoglycans due to their important role in tissue engineering and biomaterials applications, as well as in other native biological tissues such as the corneal stroma and central nervous system (1,14-16).

The specific objectives of this study are twofold. First, we investigate the effects of CS chemical composition, namely sulfation type, sulfation pattern, and molecular weight, on CS osmotic pressure under physiological conditions (0.15 M NaCl) to gain insight into the potentially relevant biomechanical function of these variations. Second, we evaluate the relative roles played by intrinsic versus electrostatic CS backbone stiffness as well as steric excluded volume interactions to gain a better understanding of the molecular origin of CS osmotic pressure. The latter aim is to aid in the development and application of analytical models of cartilage biomechanics (17-19). Toward this end, we employ a recently developed coarse-grained molecular model that enables the computation of solution conformational and thermodynamic properties of GAGs (20). The model uses systematic coarse-graining from an all-atom representation of the disaccharide building blocks of GAGs to achieve computational tractability that enables the simulation of physiologically relevant system sizes while retaining the underlying chemical identity of the sugars. In our previous work, we applied the coarse-grained model to chondroitin (CH), chondroitin 4-sulfate (C4S), chondroitin 6-sulfate (C6S), and hyaluronic acid in infinitely dilute solution and studied the effects of sulfation type, ionic strength, and pH on their conformation and titration behavior (20). In the current work, we demonstrate theoretically that the model is also directly applicable to the computation of GAG osmotic pressure, and we use it to investigate mechanistically the CS chemical composition-osmotic pressure relationship. Osmotic pressure predictions are compared with experimental data of Ehrlich and others (21), and contrasted with two well-established models of polyelectrolyte solutions-the Donnan theory and the Poisson-Boltzmann cylindrical cell model. Although the ultimate aim of this line of research is to study the physiological solution conformation and mechanical properties of aggrecan, the current investigation into the solution behavior of CS is viewed as a valuable and necessary step toward that end, both for purposes of model validation and because we believe that a fundamental understanding of the solution properties of aggrecan requires a comprehensive understanding of the properties of its biochemical constituents.