Interactions between nearest-neighboring glycosaminoglycan molecules of articular cartilage

The electrostatic interaction effects including the interaction potential, force and torque between the neighboring chondroitin sulfate glycosaminoglycan (CS-GAG) molecular chains in the bottle brush conformation of proteoglycan aggrecan are obtained as the functions of the minimum separation distance and the mutual angle between the molecular chains based on an asymptotic solution of the Poisson-Boltzmann equation that the CS-GAGs satisfy under the normal physiological conditions of articular cartilage. The present study indicates that the electrostatic interactions are not only associated intimately with the separation distance and the mutual angle, which are shown as purely exponential in separation distance and decrease with increasing mutual angle, but also dependent sensitively on the saline concentration in the electrolyte solution within the tissue. Further analysis shows that in the range of the separation distance between two neighboring CS-GAG molecular chains in the bottle brush conformation of the aggrecan in vivo (2 to approximately 4 nm), if the saline concentration in the electrolyte solution is not less than a value of concentration (approximately 0.1 M), the interactions between the molecular chains will monotonically increase with decreasing the saline concentration, however, if the saline concentration is less than the value of concentration, the relationship between the interactions and the saline concentration will not be simply monotonic. Some present results are in agreement with the existed relevant conclusions.