A molecular model of proteoglycan-associated electrostatic forces in cartilage mechanics

Journal of Biomechanical Engineering

Volumn 117, Issue 2, 1995, Pages 179-192

  Buschmann, M D ^a   Grodzinsky, A J ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CARTILAGE; ELECTRIC FIELDS; ELECTROPHYSIOLOGY; ELECTROSTATICS; IONIC STRENGTH; IONS; MACROMOLECULES; MATHEMATICAL MODELS; POLYELECTROLYTES;

DONNAN EQUILIBRIUM; ELECTROSTATIC FORCES; GLYCOSAMINOGLYCAN; POISSON BOLTZMANN EQUATION; PROTEOGLYCAN;

BIOMECHANICS;

GLYCOSAMINOGLYCAN; PROTEOGLYCAN;

ARTICLE; ARTICULAR CARTILAGE; ELECTRIC FIELD; ELECTRIC POTENTIAL; FORCE; IONIC STRENGTH; MECHANICS; MOLECULAR MODEL; OSMOSIS; PRESSURE; THEORY;

ANIMAL; BIOMECHANICS; BIOMEDICAL ENGINEERING; CARTILAGE, ARTICULAR; CATTLE; COMPARATIVE STUDY; ELECTROCHEMISTRY; IN VITRO; MODELS, BIOLOGICAL; OSMOTIC PRESSURE; PROTEOGLYCANS; SOLUTIONS; STRESS, MECHANICAL; SUPPORT, NON-U.S. GOV'T; SUPPORT, U.S. GOV'T, NON-P.H.S.; SUPPORT, U.S. GOV'T, P.H.S.;

EID: 0029294464     PISSN: 01480731     EISSN: 15288951     Source Type: Journal    
DOI: 10.1115/1.2796000     Document Type: Article

References (66)

1. Basser, P. J., and Grodzinsky, A. J., 1993, “The Donnan Model Derived From Microstructure,” Biophysical Chemistry, Vol. 46, pp. 57-68.
2. Buckwalter, J., Hunziker, E., Rosenberg, L., Coutts, R., Adams, M., and Eyre, D., 1988, “Articular Cartilage: Composition and Structure,” Woo, S. L., and Buckwalter, J. A., eds., Injury and Repair of the Musculoskeletal Soft Tissues, pp. 405-425, American Academy of Orthopaedic Surgeons, Park Ridge, IL.
3. Buschmann, Michael D., 1992, “Chondrocytes in Agarose Culture: Development of a Mechanically Functional Matrix, Biosynthetic Response to Compression, and Molecular Model of the Modulus,” PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.
4. Buschmann, M. D., Gluzband, Y. A., Grodzinsky, A. J., Kimura, J. H., and Hunziker, E. B., 1992, “Chondrocytes in Agarose Culture Synthesize a Mechanically Functional Extracellular Matrix,” J. Orthop. Res., Vol. 10, pp. 745-758.
5. Carnic, S. L., and Torric, G. M., 1984, “Statistical Mechanics of the Electrical Double Layer,” Ado. in Chem. Phys., Vol. 56, pp. 141-253.
6. Comper, W. D., 1991, “Physicochemical Aspects of Cartilage Extracellular Matrix,” Hall, B., and Newman, S., eds., Cartilage: Molecular Aspects, pp. 59-96. CRC, Boca Raton, FL.
7. Comper, W. D., and Laurent, T. C., 1978, “Physiological Function of Connective Tissue Polysaccharides,” Physiological Reviews, Vol. 58, pp. 255-315.
8. Comper, W. D., and Preston, B. N., 1974, “Model Connective Tissue Systems: A Study of Polyion-Mobile Ion and of Excluded Volume Interactions of Proteoglycans,” Biochem. J., Vol. 143, pp. 1-9.
9. Comper, W. D., and W, Williams, R. P., 1987, “Hydrodynamics of Concentrated Proteoglycan Solutions,” J. Biol. Chem., Vol. 262, pp. 13464-13471.
10. de Gennes, P. G., 1978, “Global Molecular Shapes in Polyelectrolyte Solutions,” Everett, D. H., and Vincent, B., eds., Colston Papers No. 29. Ions in Macromolecular and Biological Systems, pp. 69-79, Scientechnica, Bristol, U.K.
11. Einevoll, G., and Hemmer, P. C., 1988, “Spatial Distribution of Ions Around Rod-Like Polyelcctrolytes,” J. Chem. Phys., Vol. 89, pp. 474-482.
12. Eisenberg, S. R., and Grodzinsky, A. J., 1985, “Swelling of Articular Cartilage and Other Connective Tissues,” J. Orthop. Res., Vol. 3, pp. 148-159.
13. Eisenberg, S. R., and Grodzinsky, A. J., 1988, “Electrokinctic Micromodel of Extracellular Matrix and Other Polyelectrolyte Networks,” Physicochemical Hydrodynamics, Vol. 10, pp. 517-539.
14. Engel, J., and Furthmayr, H., 1987, “Electron Microscopy and Other Physical Methods for the Characterization of Extracellular Matrix Components: Laminin, Fibronectin, Collagen IV, Collagen VI, and Proteoglycans,” Cunningham, L. W., ed., Methods in Enzymology, Vol. 145, pp. 3-78, Academic Press, San Diego.
15. Fixman, M., 1979, “The Poisson-Boltzmann Equation and its Application to Polyelectrolytes,” J. Chem. Phys., Vol. 70, pp. 4995-5005.
16. Fletcher, P. D. I., Robinson, B. H., and Tabony, J., 1988, “A Quasielastic Neutron-Scattering Study of the Molecular Mobility of Water Associated with a Protein Both in Aqueous Solution and Adjacent to a Charged Surfactant,” Biochim. Biophys. Acta, Vol. 954, pp. 27-36.
17. Flory, P. J., 1953, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY.
18. Frank, H. H., Grodzinsky, A. J., Phillips, S. L., and Grimshaw, P. E., 1990, “Physicochemical and Bioelectrical Determinants of Cartilage Material Properties,” Mow, V. C., Ratcliffe, A., and Woo, S. L. Y., eds., Biomechanics of Diarthroidal Joints, Vol. 1, pp. 261-282, Springer-Verlag, New York.
19. Fuoss, R. M., Katchalsky, A., and Lifson, S., 1951, “The Potential of an Infinite Rod-like Molecule and the Distribution of Counterions,” Proc. Nat. Acad. Sci. (U.S.), Vol. 37, pp. 579-589.
20. Grynpas, M. D., Eyre, D. R., and Kirschner, D. A., 1980, “Collagen Type II Differs from Type I in Native Molecular Packing,” Biochem. Biophys. Acta, Vol. 626, pp. 346-355.
21. Guldbrand, L. G, Nilsson, L., and Nordenskiold, L., 1986, “A Monte Carlo Simulation of Electrostatic Forces Between Hexagonally Packed DNA Double Helices,” J. Chem. Phys., Vol. 85, pp. 6686-6698.
22. Gur, Y., Ravina, I., and Babchin, A. J., 1978, “On the Electrical Double Layer Theory 1. A Numerical Method for Solving a Generalized Poisson-Boltzmann Equation,” J. Coll. Int. Sci., Vol. 64, pp. 326-332.
23. Heincgard, D., and Oldberg O, 1989, “Structure and Biology of Cartilage and Bone Matrix Noncollagenous Macromoleculcs,” FASEB J., Vol. 3, pp. 2042-2051.
24. Hodge, W. A., Fijan, R. S., Carlson, K. L., Burgess, R. G., Harris, W. H., and Mann, R. W., 1986, “Contact Pressures in the Human Hip Joint Measured in vivo,” Proc. Natl. Acad. Sci. USA, Vol. 83, pp. 2879-2883.
25. Israelachvili, J. N., 1991, Intermolecular and Surface Forces, Academic Press, New York, NY, 2nd edition.
26. Jonsson, B., Wennerstrom, H., and Halle, B., 1980, “Ion Distributions in Lamellar Liquid Crystals. A Comparison Between Results from Monte Carlo Simulations and Solutions of the Poisson-Boltzmann Equation,” J. Phys. Chem., Vol. 84, pp. 2179-2185.
27. Katchalsky, A., 1971, “Polyclectrolytes,” Pure Appl. Chem., Vol. 26, pp. 327-373.
28. Katchalsky, A., Alexandrowicz, Z., and Kcdem, O., 1966, “Polyclectro-lyte Solutions,” Conway, B. E., and Barrades, R. G., eds., Chemical Physics of Ionic Solutions, pp. 295-346, Wiley, New York.
29. Kimura, J. H., Lohmander, L. S., and Hascall, V. C., 1984, “Studies on the Biosynthesis of Cartilage Proteoglycan in a Model System of Cultured Chondrocytes from the Swarm Rat Chondrosarcoma,” J. Cell Biochem., Vol. 26, pp. 261-278.
30. Lai, W. M., Hou, J. S., and Mow, V. C., 1991, “A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage,” ASME Journal of Biomechanical Engineering, Vol. 113, pp. 245-258.
31. Lesperance, L. M., Gray, M. L., and Burstein, D., 1992, “Determination of Fixed Charge Density in Cartilage Using Nuclear Magnetic Resonance,” J. Orthop. Res., Vol. 10, p. 1-14.
32. Manning, G. S., 1969, “Limiting Laws and Counterion Condensation in Polyclectrolyte Solutions I. Colligative Properties,” J. Chem. Phys., Vol. 51, pp. 924-933.
33. Marcus, R. A., 1955, “Calculation of Thermodynamic Properties of Polyclectrolytes,” 7. Chem. Phys., Vol. 23, pp. 1057-1068.
34. Maroudas, A., 1979, “Physico-chemical Properties of Articular Cartilage,” Freeman, M. A. R., ed., Adult Articular Cartilage, 2nd cd., pp. 215-290, Pitman, Tunbridge Wells, England.
35. Maroudas, A., and Bannon, C., 1981, “Measurement of Swelling Pressures in Cartilage and Comparison with the Osmotic Pressure of Constituent Proteoglycans,” Biorheology, Vol. 18, pp. 619-632.
36. Maroudas, A., Weinberg, P. D., Parker, K. H., and Winlove, C. P., 1988, “The Distributions and Diffusivities of Small Ions in Chondroitin Sulphate, Hyaluronate, and Some Proteoglycan Solutions,” Biophysical Chemistry, Vol. 32, pp. 257-270.
37. Maroudas, A., Wachtcl, E., Grushko, G., Katz, E. P., and Weinberg, P., 1991, “The Effect of Osmotic and Mechanical Pressures on Water Partitioning in Articular Cartilage,” Biophys. Biochem. Acta, Vol. 1073, pp. 285-294, 1991.
38. McCaskill, J. S., and Fackercll, E. D., 1988, “Painleve Solution of the Poisson-Boltzmann Equation for a Cylindrical Polyelectrolyte in Excess Salt Solution,” B. Chem. Soc. Faraday Trans. 2, Vol. 84, pp. 161-179.
39. McLaughlin, S., 1989, “The Electrostatic Properties of Membranes,” Annu. Rev. Biophys. Biophys. Chem., Vol. 89, pp. 113-136.
40. Mclcher, J. R., 1981, Continuum Electromechanics, MIT Press, Cambridge, MA.
41. Morgelin, M., Paulsson, M., Malmstrom, A., and Heinegard, D., 1989, “Shared and Distinct Structural Features of Interstitial Proteoglycans from Different Bovine Tissues Revealed by Electron Microscopy,” 7. Biol. Chem., Vol. 264, pp. 12080-12090.
42. Mow, V., and Rosenwasscr, M., 1988, “Articular Cartilage: Biomechanics,” Woo, S. L., and Buckwalter, J. A., eds., Injury and Repair of the Musculoskeletal Soft Tissues, pp. 427-463, American Academy of Orthopaedic Surgeons, Park Ridge, IL.
43. Muir, I. H. M., 1979, “Biochemistry,” Freeman, M. A. R., ed., Adult Articular Cartilage, 2nd ed., pp. 145-214, Pitman, Tunbridge Wells, England.
44. Nagasawa, M., and Kagawa, I., 1957, “Colligative Properties of Polyelectrolyte Solutions. IV. Activity Coefficient of Sodium Ion.” B. Polymer Sci., Vol. 25, pp. 61-76.
45. Ogstcn, A. G., Preston, B. N., and Wells, J. D., 1973, “On the Transport of Compact Particles through Solutions of Chain-polymers,” Proc. R. Soc. Lond. A, Vol. 333, pp. 297-316.
46. Oosawa, F., 1971, Polyelectrolytes, Marcel Dekker, New York, NY, First Edition.
47. Overbcek, J. T. G., 1956, “The Donnan Equilibrium,” Prog. Biophys. Biophys. Chem., Vol. 6, pp. 58-84.
48. Parker, K. H., Winlove, C. P., and Maroudas, A., 1988, “The Theoretical Distributions and Diffusivities of Small Ions in Chondroitin Sulphate and Hyaluronate,” Biophysical Chemistry, Vol. 32, pp. 271-282.
49. Peitzsch, R. M., and Reed, W. F., 1992, “High Osmotic Stress Behavior of Hyaluronate and Heparin,” Biopolymers, Vol. 32, pp. 219-238.
50. Preston, B. N., Snowden, J. M., and Houghton, K. T., 1972, “Model Connective Tissue Systems: The Effect of Proteoglycans on the Distribution of Small Non-electrolytes and Micro-ions,” Biopolymers, Vol. 11, pp. 1645-1659.
51. Ramanathan, G. V., 1985, “The Cell Model for Polyclectrolytes with Added Salt,” 7. Chem. Phys., Vol. 82, pp. 1482-1491.
52. Rau, D. C., and Parscgian, V. A., 1990, “Direct Measurements of Forces Between Linear Polysaccharides Xanthan and Schizophyllan,” Science, Vol. 249, pp. 1278-1281.
53. Rinaudo, M., 1978, “Interchain Correlation Observed in Neutron Scattering by Polyelectrolyte Solutions,” Everett, D. H., and Vincent, B., eds., Colston Papers No. 29, Ions in Macromolecular and Biological Systems, pp. 79-80, Scicntechnica, Bristol, UK.
54. Robinson, R. A., and Stokes, R. H., 1968, Electrolyte Solutions, Butter-worths, London.
55. Sah, R. L-Y., 1991, Personal Communication.
56. Sanfield, A., 1968, Introduction to the Thermodynamics of Charged and Polarized Layers, Wiley, New York, NY.
57. Shaw, M., 1976, “Interpretation of Osmotic Pressure,” Biophys. J., Vol. 16, pp. 43-57.
58. Svensson, B., Jonsson, B., and Woodward, C. E., 1990, “Monte Carlo Simulations of an Electrical Double Layer,” J. Phys. Chem., Vol. 94, pp. 2105-2113.
59. Tanford, C., 1961, Physical Chemistry of Macromoleculcs, Wiley, New York, NY.
60. Upholt, W. B., and Olsen, B. R., 1991, “The Active Genes of Cartilage,” Hall, B., and Newman, S., eds., Cartilage: Molecular Aspects, pp. 43-79, CRC, Boca Raton, FL.
61. Urban, J. P. G., Maroudas, A., Baytiss, M. T., and Dillon, J., 1979, “Swelling Pressures of Proteoglycans at the Concentrations Found in Cartilagcnous Tissues,” Biorheology, Vol. 16, pp. 447-464.
62. Wells, J. D., 1973, “Salt Activity and Osmotic Pressure in Connective Tissue. I. A Study of Solutions of Dextran Sulphate as a Model System,” Proc. R. Soc. Lond. B., Vol. 183, pp. 399-419.
63. Wells, J. D., 1973, “Thermodynamics of Polyclectrolyte Solutions. An Empirical Extension of the Manning Theory to Finite Salt Concentrations,” Biopolymers, Vol. 12, pp. 223-227.
64. Wennerstrom, H., Jonsson, B., and Linsc, P., 1982, “The Cell Model for Polyelectrolyte Systems. Exact Statistical Mechanical Relations, Monte Carlo Simulations, and the Poisson-Boltzmann Approximation,” J. Chem. Phys., Vol. 76, pp. 4665-4670.
65. Williams, R. P. W., and Compcr, W. D., 1990, “Osmotic Flow Caused by Polyelcctrolytes,” Biophysical Chemistry, Vol. 36, pp. 223-234.
66. Zimm, B. H., and Le Bret, M., 1983, “Counter-ion Condensation and System Dimensionality,” J. Biomolecular Structure and Dynamics, Vol. 1, pp. 461-471.