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Peter M. Pinsky, Hamed Hatami-Marbini; Modeling Collagen-Proteoglycan Structural Interactions in the Corneal Stroma. Invest. Ophthalmol. Vis. Sci. 2011;52(14):4382.
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© ARVO (1962-2015); The Authors (2016-present)
Structural interactions between collagens and proteoglycans (PGs) are important determinants of mechanical properties in connective tissues, including the corneal stroma. We use the detailed three-dimensional arrangement of collagen fibrils and leucine-rich repeat PGs revealed by recent imaging to create a molecular-level biophysical model to explain stromal shear stiffness, stromal swelling behavior and the origin of forces which are responsible for the maintenance of the collagen lattice.
Recent imaging has suggested PGs bind collagen fibrils at equidistant locations along the fibrils and extend a linear chain of repeating disaccharides orthogonal to the fibril. Intrafibrillar bridges may be formed by duplexing of the glycosaminoglycan (GAG) chains. We consider a unit cell of stroma in thermodynamic equilibrium and examine two feasible collagen-PG arrangements based on nearest neighbor (Maurice, 1962) and next-nearest neighbor (Müller et al., 2004) topological organization. The GAGs, which are ionized with net negative charge under physiological conditions, are represented by cylindrical domains with fixed charge density and the mobile ion concentrations in the matrix fluid have a Boltzmann distribution. The electrostatic potential is determined from solution of the Poisson-Boltzmann equation and the resulting free energy is augmented for entropic and enthalpic stretching of the GAG chains.
The model is validated by estimating the stromal shear stiffness by determining the energy cost to deform the unit cells in shear thereby changing the interfibrillar spacings. The results are compared to direct torsional measurement of the shear stiffness of a lamellar slice of human cornea. The model is similarly employed in a transverse (thickness) deformation mode to predict swelling and osmotic pressures as a function of GAG charge density and ionic concentration. Predictions for the thermodynamic restoring force that is exerted on collagen fibrils perturbed from the collagen lattice are also determined.
The regular lattice of stromal fibrils interconnected by an organized system of negatively charged GAG bridges creates an electrolytic gel-like composite structure that can be modeled in terms of free energy and solved using a numerical approach. Collagen lattice forces, stromal shear stiffness and swelling pressure can be expressed in terms of intrinsic tissue properties and molecular topology. The model could be important for providing guiding principles for tissue engineering of stromal equivalents.
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