Modeling Collagen-Proteoglycan Structural Interactions in the Human Cornea

Abstract

The cornea is a supremely organized connective tissue making it ideal for modeling and probing possible roles of collagen-PG interactions in the extracellular matrix. The cornea can be viewed as a reinforced electrolyte gel involving molecular-scale interactions between collagen fibrils, proteoglycans (PGs) and the mobile ions in the interfibrillar space. The swelling property of the tissue cannot be adequately predicted by Donnan theory for osmotic pressure. We propose an alternative unit cell approach based on a thermodynamic framework that employs a mean-field approximation for the electrostatic free energy and which accounts for a non-uniform electrostatic potential. The model is used to show that the equilibrium swelling pressure can be explained when the geometrical effect of electrolyte exclusion due to collagen fibril volume is considered. The model is further refined by dividing the PGs into collagen fibril coating and volumetric partitions. The model suggests that the PG coatings overlap at low hydration and set up repulsive forces that may act to maintain the collagen lattice order. Finally, we introduce a molecular-level unit cell in which volumetric domains within the unit cell are associated with the macromolecular GAGs and results from the continuum and molecular-level models are compared.

References

  1. Buschmann MD, Grodzinsky AJ (1995) A molecular model of proteoglycan-associated electrostatic forces in cartilage mechanics. J Biomech Eng 2:179–192 CrossRefGoogle Scholar
  2. Che J, Dzubiella J, Li B, McCammom JA (2008) Electrostatic free energy and its variations in implicit solvent models. J Phys Chem B 112:3058–3069 CrossRefGoogle Scholar
  3. Elliott GF, Hodson SA (1998) Cornea, and the swelling of polyelectrolyte gels of biological interest. Rep Math Phys 61:1325–1365 Google Scholar
  4. Fatt I (1968) Dynamics of water transport in the corneal stroma. Exp Eye Res 7:402–412 CrossRefGoogle Scholar
  5. Fogolari F, Briggs JM (1997) On the variational approach to Poisson-Boltzmann free energies. Chem Phys Lett 281:135–139 CrossRefGoogle Scholar
  6. Fratzl P, Daxer A (1993) Structural transformation of collage fibrils in corneal stroma during drying. Biophys J 64:1210–1214 CrossRefGoogle Scholar
  7. Hart RW, Farrell RA (1971) Structural theory of the swelling pressure of corneal stroma in saline. Bull Math Biophys 33:165–186 CrossRefGoogle Scholar
  8. Hedbys BO, Dohlman C (1963) A new method for the determination of the swelling pressure of the corneal stroma in in vitro. Exp Eye Res 2:122–129 CrossRefGoogle Scholar
  9. Hedbys BO, Mishima S (1966) The thickness-hydration relationship of the cornea. Exp Eye Res 5:221–228 CrossRefGoogle Scholar
  10. Hodson S (1971) Why the cornea swells. J Theor Biol 33:419–427 CrossRefGoogle Scholar
  11. Jin M, Grodzinsky AJ (2001) Effect of electrostatic interactions between glycosaminoglycans on the shear stiffness of cartilage: a molecular model and experiments. Macromolecules 34:8330–8339 CrossRefGoogle Scholar
  12. Katchalsky A, Michaeli I (1955) Polyelectrolyte gels in salt solutions. J Polym Sci 15:69–86 CrossRefGoogle Scholar
  13. Lewis PN, Pinali C, Young RD, Meek KM, Quantock AJ, Knupp C (2010) Structural interactions between collagen and proteoglycans are elucidated by three-dimensional electron tomography of bovine cornea. Structure 18:239–245 CrossRefGoogle Scholar
  14. Meek KM, Leonard DW (1993) Ultrastructure of the corneal stroma: a comparative study. Biophys J 64:273–280 CrossRefGoogle Scholar
  15. Muller LJ, Pels E, Schurmans L, Vrensen G (2004) A new three-dimensional model of the organization of proteoglycans can collagen fibrils in the human corneal stroma. Exp Eye Res 78:493–501 CrossRefGoogle Scholar
  16. Olsen T, Sperling S (1987) The swelling pressure of the human corneal stroma as determined by a new method. Exp Eye Res 44:481–490 CrossRefGoogle Scholar
  17. Scott JE (1992) Morphometry of cupromeronic blue-stained proteoglycan molecules in animal corneas, versus that of purified proteoglycans stained in vitro, implies that tertiary structures contribute to corneal ultrastructure. J Anat 180:155–164 Google Scholar
  18. Twersky V (1975) Transparency of pair-correlated, random distributions of small scatterers, with applications to the cornea. J Opt Soc Am A 65:524–530 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Xi Cheng
    • 1
  • Hamed Hatami-Marbini
    • 1
    • 2
  • Peter M. Pinsky
    • 1
  1. 1.Department of Mechanical EngineeringStanford UniversityStanfordUSA
  2. 2.School of Mechanical and Aerospace EngineeringOklahoma State UniversityStillwaterUSA

Personalised recommendations