Abstract
The transparency of the human cornea depends on the regular lattice arrangement of the collagen fibrils and on the maintenance of an optimal hydration--the achievement of both depends on the presence of stromal proteoglycans (PGs) and their linear sidechains of negatively charged glycosaminoglycans (GAGs). Although the GAGs produce osmotic pressure by the Donnan effect, the means by which they exert positional control of the lattice is less clear. In this study, a theoretical model based on equilibrium thermodynamics is used to describe restoring force mechanisms that may control and maintain the fibril lattice and underlie corneal transparency. Electrostatic-based restoring forces that result from local charge density changes induced by fibril motion, and entropic elastic restoring forces that arise from duplexed GAG structures that bridge neighbouring fibrils, are described. The model allows for the possibility that fibrils have a GAG-dense coating that adds an additional fibril force mechanism preventing fibril aggregation. Swelling pressure predictions are used to validate the model with results showing excellent agreement with experimental data over a range of hydration from 30 to 200% of normal. The model suggests that the electrostatic restoring force is dominant, with the entropic forces from GAG duplexes being an order or more smaller. The effect of a random GAG organization, as observed in recent imaging, is considered in a dynamic model of the lattice that incorporates randomness in both the spatial distribution of GAG charge and the topology of the GAG duplexes. A striking result is that the electrostatic restoring forces alone are able to reproduce the image-based lattice distribution function for the human cornea, and thus dynamically maintain the short-range order of the lattice.