Abstract
The radial distribution function characterizing the spatial organization of the long fibrils of connective tissue is obtained by mathematical analysis of molecular models. The models are based on the assumption that polymeric chains form bridges between the fibrils, thereby providing the long range interactions responsible for the quasi-ordered spatial disposition of the fibrils. The theory is applied to rabbit cornea for which an empirical radial distribution has been obtained previously by analysis of electron micrographs. General agreement is found between theory and experiment for parameter values that are thought to be representative of stroma. The analysis constitutes a step toward the development of the physical basis of the ultrastructure of connective tissue and the way in which that structure affects physiological behavior.
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Literature
Berlin, T. H. and M. Kac. 1952. “The Spherical Model of a Ferromagnet.”Phys. Rev.,86, 821–835.
Bernardi, G. 1957. “Size and Shape of Cartilage Mucoprotein.”Nature,180, 93–94.
— 1957. “The Molecular Size, Shape and Weight of Mucoprotein from Cartilage.”Biochem. Biophys. Acta.,26, 47–52.
Cessi, C. and G. Bernardi. 1965. “The Kinetics of Enzymatic Degradation and the Structure of Protein Polysaccharide Complexes of Cartilage,” inStructure and Function of Connective and Skeletal Tissue. NATO Advanced Study Inst. London: Butter-worths.
Clark, Janet H. 1932. “A Method for Measuring Elasticityin Vivo and the Results Obtained on the Eyeball at Different Intraocular Pressures.”Am. J. Physiol.,101, 474–481.
Desloge, Edward H. 1966.Statistical Physics, p. 18. New York: Holt Rinehart and Winston, Inc.
Duke-Elder, S. Ed. 1961.A System of Ophthalmology. Vol. II, pp. 106–107. St. Louis, Missouri: C. V. Mosby Co., Pub.
Francois, J., M. Rabaey and G. Vandermeerssche. 1954. “L'ultrastructure des tissus oculaires au microscope électronique. II. Etude de la cornée et de la sclérotique.”Ophthalmologica,120, 74–85.
Goldman, J. N. and G. B. Benedek. 1967. “The Relationship Between Morphology and Transparency in the Nonswelling Corneal Stroma of the Shark.”J. Invest. Ophthal.,6, 574–600.
Hart, R. W. and R. A. Farrell. 1969. “Light Scattering in the Cornea.”J. Opt. Soc. Am.,59, (June), 766–774.
Huxley, H. E. 1965. “The Mechanism of Muscular Contraction.”Sci. Am. (Dec.), p. 21.
Jakus, M. A. 1964.Ocular Fine Structure, plate 25. Boston: Little Brown & Company.
James, H. M. 1947. “Statistical Properties of Networks of Flexible Chains.”J. Chem. Phys.,15, 651–668.
Langham, M. E., R. W. Hart and J. Cox. 1969. “The Interaction of Collagen and Mucopolysaccharides,” inThe Cornea. M. E. Langham, ed. Baltimore: Johns Hopkins University Press (in press).
Laurent, T. and A. Anseth. 1961. “Studies on Corneal Mucopolysaccharides.”Exp. Eye Res.,1, 99–105.
Mathews, M. B. 1965. “The Interaction of Collagen and Acid Mucopolysaccharides.”Biochem J.,96, 710–716.
— 1967. “Biophysical Aspects of Acid Mucopolysaccharides Relevant to Connective Tissue Structure and Function,” inConnective Tissue, pp. 304–329. B. M. Wagner and D. E. Smith, eds. Baltimore: Williams and Wilkins.
Mathews, M. B. and I. Lozaityte. 1958. “Sodium Chondroitin Sulfate-Protein Complexes of Cartilage. I. Molecular Weight and Shape.”Arch. Biochem. Biophys.,74, 158.
Maurice, D. M. 1957. “The Structure and Transparency of the Cornea.”J. Physiol.,136, 263–286.
— 1962. Chap. 6 ofThe Eye. Vol. I, H. Davson, Ed., New York: Academic Press.
Montroll, E. W., T. H. Berlin and R. W. Hart. 1952. “Fonctions Delta et Intégrals Gaussiennes en Mécanique Statistique.”Extr. Comptes Rendus, Réunion de Chemie Physique, pp. 211–223.
Partridge, S. M., H. F. Davis and G. S. Adair. 1960. “The Constitution of the Chondroitin Sulphate-Protein Complex in Cartilage.”Biochem J.,79, 15–26.
Schubert, M. and D. Hamerman. 1968.A Primer on Connective Tissue Biochemistry (especially Chapters 3 and 5). Philadelphia: Lea and Febingek.
Schwarz, W. and D. Graf Keyserlingk. 1966. “Über Die Feinstruktur Der Menschlichen Cornea, Mit Besonderer Berücksichtigung Des Problems Der Transparenz.”Z. Zellforsch.,73, 540–548.
Tanford, Charles. 1967.Physical Chemistry of Macromolecules, p. 167. New York: John Wiley and Sons.
Webber, R. V. and S. T. Bayley. 1956. “Some Observations on the Molecular Form of Chondroitin Sulphate.”Canad. J. Biochem. and Biophys.,34, 963–1005.
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Farrell, R.A., Hart, R.W. On the theory of the spatial organization of macromolecules in connective tissue. Bulletin of Mathematical Biophysics 31, 727–760 (1969). https://doi.org/10.1007/BF02477784
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DOI: https://doi.org/10.1007/BF02477784