Type-I collagen fibrils: From growth morphology to local order

  • Jean Charvolin
  • Jean-François SadocEmail author
Regular Article


The length of type-I collagen fibrils in solution increases through the development and progress of pointed tips appearing successively at the two ends of an axis-symmetric shaft with constant diameter. Those tips, respectively fine (\(\alpha\)) or coarse (\( \beta\)) have opposite molecular orientations. The \(\alpha\)-pointed tips, the first to appear, are particularly remarkable as they all show, on most of their length, a common parabolic profile which stays constant during the growth. Assuming that the latter occurs by lateral accretion of individual molecules in staggered configuration, we propose to give account of this prominent morphological feature along a purely geometrical argument, the profile of a tip being linked to the shape of the trajectories followed all along the accretion process. Among several possible trajectories, Fermat spirals lead to a parabolic profile in perfect agreement with the one observed for \(\alpha\)-pointed tips. This is to be put in relation with the presence of such spirals in phyllotactic patterns which ensure the best packing efficiency in cases of axis-symmetry, which is indeed that of dense collagen fibrils. Moreover, those patterns are structured by concentric circles of dislocations, constitutive of the structure itself, whose behaviour might contribute to the mechanical properties of the fibrils.

Graphical abstract


Living systems: Biological Matter 


  1. 1.
    A. Leforestier, F. Livolant, J. Mol. Biol. 396, 384 (2010)CrossRefGoogle Scholar
  2. 2.
    A.J. Hodge, F.O. Smith, Proc. Natl. Acad. Sci. U.S.A. 46, 186 (1960)ADSCrossRefGoogle Scholar
  3. 3.
    A.J. Hodge, J.A. Petruska, in Aspects of Protein Structure, edited by G.N. Ramachandran (Academic Press, New York, 1963)Google Scholar
  4. 4.
    J.A. Petruska, A.J. Hodge, Proc. Natl. Acad. Sci. U.S.A. 51, 871 (1964)ADSCrossRefGoogle Scholar
  5. 5.
    J.W. Smith, Nature 219, 157 (1968)ADSCrossRefGoogle Scholar
  6. 6.
    J. Woodhead-Galloway, Acta Crystallogr. B 33, 1212 (1977)CrossRefGoogle Scholar
  7. 7.
    A.L. Bailey, N.D. Light, E.D.T. Atkins, Nature 288, 408 (1980)ADSCrossRefGoogle Scholar
  8. 8.
    J.P. Orgel, T.J. Wess, A. Miller, Structure 8, 137 (2000)CrossRefGoogle Scholar
  9. 9.
    D.J. Hulmes, T.J. Wess, D.J. Prockop, P. Fratz, Biophys. J. 68, 1661 (1995)ADSCrossRefGoogle Scholar
  10. 10.
    D.J. Hulmes, J.-C. Jesior, A. Miller, C. Berthet-Colominas, C. Wolff, Proc. Natl. Acad. Sci. U.S.A. 78, 3567 (1981)ADSCrossRefGoogle Scholar
  11. 11.
    J. Charvolin, J.-F. Sadoc, Biophys. Rev. Lett. 8, 33 (2013)CrossRefGoogle Scholar
  12. 12.
    G.C. Woods, M.K. Keech, Biochem. J. 75, 588 (1960)CrossRefGoogle Scholar
  13. 13.
    G.C. Woods, Biochem. J. 75, 598 (1960)CrossRefGoogle Scholar
  14. 14.
    G.C. Woods, Biochem. J. 75, 605 (1960)CrossRefGoogle Scholar
  15. 15.
    R.L. Trelstad, K. Hayashi, J. Gross, Proc. Natl. Acad. Sci. U.S.A. 73, 4027 (1976)ADSCrossRefGoogle Scholar
  16. 16.
    R.R. Bruns, D.J.S. Hulmes, S.F. Terrien, J. Gross, Proc. Natl. Acad. Sci. U.S.A. 76, 313 (1979)ADSCrossRefGoogle Scholar
  17. 17.
    D.J.S. Hulmes, R.R. Bruns, J. Gross, Proc. Natl. Acad. Sci. U.S.A. 80, 388 (1983)ADSCrossRefGoogle Scholar
  18. 18.
    R.A. Gelman, B.R. Williams, K.A. Piez, J. Biol. Chem. 254, 180 (1979)Google Scholar
  19. 19.
    D.E. Birk, E.I. Zycband, D.E. Winklemann, R.L. Trelstad, Proc. Natl. Acad. Sci. U.S.A. 86, 4549 (1989)ADSCrossRefGoogle Scholar
  20. 20.
    K.E. Kadler, Y. Hojima, D.J. Prockop, Biochem. J. 268, 339 (1990)CrossRefGoogle Scholar
  21. 21.
    Nima Saedi, Thesis, North Western University (2009)Google Scholar
  22. 22.
    J.W. Weisel, C. Nagaswami, L. Makowski, Proc. Natl. Acad. Sci. U.S.A. 84, 8991 (1987)ADSCrossRefGoogle Scholar
  23. 23.
    J. Charvolin, J.-F. Sadoc, Biophys. Rev. Lett. 9, 225 (2014)CrossRefGoogle Scholar
  24. 24.
    S. Cameron, L. Kreplak, A.D. Rutenberg, Soft Matter 14, 4772 (2018)ADSCrossRefGoogle Scholar
  25. 25.
    G. Grason, Rev. Mod. Phys. 87, 401 (2015)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    K.E. Kadler, D.F. Holmes, J.A. Trotter, J.A. Chapman, Biochem. J. 316, 1 (1996)CrossRefGoogle Scholar
  27. 27.
    D.F. Holmes, J.A. Chapman, D.J. Prockop, K.E. Kadler, Proc. Natl. Acad. Sci. U.S.A. 89, 9855 (1992)ADSCrossRefGoogle Scholar
  28. 28.
    D.J. Prockop, Fertala, J. Struct. Biol. 122, 111 (1998)CrossRefGoogle Scholar
  29. 29.
    A. Fertala, D.F. Holmes, K.E. Kadler, A.L. Sieron, J. Biol. Chem. 271, 14864 (1996)CrossRefGoogle Scholar
  30. 30.
    F.H. Silver, R.L. Trelstad, J. Biol. Chem. 255, 9427 (1980)Google Scholar
  31. 31.
    J. Parkinson, K.E. Kadler, A. Brass, J. Mol. Biol. 247, 823 (1994)Google Scholar
  32. 32.
    D. Silver, J. Miller, R. Harrison, D.J. Prockop, Proc. Natl. Acad. Sci. U.S.A. 89, 9860 (1992)ADSCrossRefGoogle Scholar
  33. 33.
    I.N. Ridley, Math. Biosci. 58, 129 (1982)MathSciNetCrossRefGoogle Scholar
  34. 34.
    J.-F. Sadoc, N. Rivier, J. Charvolin, Acta Crystallogr. A 68, 470 (2012)CrossRefGoogle Scholar
  35. 35.
    S. Douady, Y. Couder, Phys. Rev. Lett. 68, 2098 (1992)ADSCrossRefGoogle Scholar
  36. 36.
    N. Rivier, J.-F. Sadoc, J. Charvolin, Eur. Phys. J. E 39, 7 (2016)CrossRefGoogle Scholar
  37. 37.
    T. Gutsmann, G.E. Fantner, M. Venturoni, A. Ekani-Nikodo, J.B. Thompson, J.H. Kindt, D.E. Morse, D. Kuchnir Fygenso, P.K. Hansma, Biophys. J. 84, 2593 (2003)CrossRefGoogle Scholar
  38. 38.
    I.R. Bruss, G. Grason, Proc. Natl. Acad. Sci. U.S.A. 109, 10781 (2012)ADSCrossRefGoogle Scholar
  39. 39.
    N. Rivier, J. Phys.: Condens. Matter 4, 913 (1992)Google Scholar
  40. 40.
    S. Douady, Y. Couder, J. Theor. Biol. 178, 255 (1996)CrossRefGoogle Scholar
  41. 41.
    H.N. Yoshikawa, C. Mattis, P. Massia, G. Rousseaux, S. Douady, Eur. Phys. J. E 33, 11 (2010)CrossRefGoogle Scholar
  42. 42.
    J. Doucet, F. Briki, C. Pichon, L. Gumez, S. Bensamoun, J.-F. Sadoc, J. Struct. Biol. 173, 197 (2011)CrossRefGoogle Scholar
  43. 43.
    D.J. McBride, V. Choe, J.R. Shapiro, B. Brodsky, J. Mol. Biol. 270, 275 (1997)CrossRefGoogle Scholar
  44. 44.
    D.J.S. Hulmes, A. Miller, Nature 282, 878 (1979)ADSCrossRefGoogle Scholar
  45. 45.
    J.P. Orgel, T.C. Irving, A. Miller, T.J. Wess, Proc. Natl. Acad. Sci. U.S.A. 103, 9001 (2006)ADSCrossRefGoogle Scholar
  46. 46.
    V. Sasisekharan, M. Bansa, Curr. Sci. 59, 863 (1990)Google Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratoire de Physique des Solides (CNRS-UMR 8502), Bât. 510Université Paris-Sud (Paris-Saclay)Orsay cedexFrance

Personalised recommendations