Electrostatic Contribution of the Proteoglycans to the In-Plane Shear and Compressive Stiffness of Corneal Stroma

The extracellular matrix (ECM) is a fibrous structure embedded in an aqueous gel. The mechanical and electrostatic interactions of the ECM constituents, i.e. collagen fibers and proteoglycans (PGs), define the structure and mechanical response of connective tissues (CTs) such as cornea and articular cartilage. Proteoglycans are complex macromolecules consisting of linear chains of repeating gylcosaminoglycans (GAGs) which are covalently attached to a core protein. PGs can be as simple as decorin with a single GAG side chain or as complex as aggrecan with many GAGs. Decorin is the simplest small leucine-rich PG and is the main PG inside the corneal stroma. It has an arch shape and links non-covalently at its concave surface to the collagen fibrils. It has been shown that while collagen fibers inside the extracellular matrix resist the tensile forces, the negatively charged glycosaminoglycans and their interaction with water give compressive stiffness to the tissue. The role of PGs in biomechanical properties of the connective tissues has mainly been studied in order to explore the behavior of articular cartilage [1], which is a CT with large and highly negatively charged PGs, aggrecans. In order to explain the role of PGs in this tissue, it is commonly assumed that their contribution to the CT elasticity is because of both the repulsive forces between negatively charged GAGs and GAG interactions with free mobile charges in the ionic bath. The electrostatic contribution to the shear and compressive stiffness of cartilage is modeled by approximating GAGs as charged rods [1]. The Poisson-Boltzmann equation is used to compute the change in electrical potential and mobile ion distributions which are caused by the macroscopic deformation.