Osmotic pressure of aqueous chondroitin sulfate solution: a molecular modeling investigation

Abstract

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.

FIGURE 1

Schematic (left) and atomic force microscope image (right) of a single aggrecan molecule, illustrating the core protein main chain and the grafted GAG side chains (cp, core protein; CS, chondroitin sulfate; KS, keratan sulfate; N, N-terminal domain; C, carboxy-terminal domain; G1, globular domain 1; G2, globular domain 2; G3, globular domain 3; and IGD, interglobular domain). Images are courtesy of Laurel Ng (12).

FIGURE 2

Disaccharide repeat units of CH, C4S, and C6S.

FIGURE 3

Definition of the coarse-grained model bonded backbone structure (thick solid lines) based on the all-atom disaccharide representation for the (top) β1,3 and (bottom) β1,4 linkages.

FIGURE 4

Dependence of fully sulfated C4S osmotic pressure on polymer concentration for various molecular weights (4–32 disaccharides or 1.8–14.6 kDa) at physiological ionic strength (0.15 M). Statistical error bars are smaller than the symbols.

FIGURE 5

Reservoir ionic-strength dependence of C4S osmotic pressure (16-disaccharides). Statistical error bars are smaller than the symbols.

FIGURE 6

Effect of 4- vs. 6-sulfation (left, 16-disaccharides) and 4-sulfation pattern (right, 32-disaccharides) on osmotic pressure at physiological ionic strength (0.15 M NaCl). Statistical error bars are smaller than the symbols.

FIGURE 7

(a) Osmotic pressure of C4S compared with C4S models assuming rigid (C4S-RIGID) and freely rotating (C4S-FRC) glycosidic torsion angles at 0.15 and 1.0 M ionic strength (20-disaccharides) and (b) ratio of mean-square end-to-end distance to mean-square radius of gyration for the three models. The osmotic pressure of the C4S and the C4S-RIGID models nearly coincide at 1 M ionic strength in a and the conformation of the C4S-RIGID model is shown only once in b because it is ionic-strength independent. Statistical error bars are smaller than the symbols in a and b.

FIGURE 8

C4S osmotic-pressure (16-disaccharides) dependence on ionic strength with the repulsive LJ potential activated (DH-LJ) and deactivated (DH). Differences are everywhere <1% for 0.15 M ionic strength. Statistical error bars are smaller than the symbols.

FIGURE 9

Experimental (MW unknown; 80% sulfated; 30% C6S, and 70% C4S) (21) CS osmotic pressure compared with (a) coarse-grained molecular model (10-, 20-, and 40-disaccharides; 80% sulfated, f = 0.8; random copolymer, λ = 0) and (b) the Donnan theory, the PB cylindrical cell model (a = 5.5 Å; d = 5 Å), and the mean-field theory estimate for the steric excluded volume contribution (SEVC) to Π.