The transverse structure of collagen

Abstract

Collagen is the principal constituent of extra-cellular, connective tissue. It is a tightly-packed but flexible bundle of proteins that constitutes a material. The collagen molecule is a triple helix made of three, intertwined polypeptide chains, associated with and its rational convergents. Accordingly, the collagen fibril, a long, periodic bundle of finite collagen molecules, has a transverse structure based on two underlying, perpendicular hexagonal lattices. It is the Archimedean, square-triangle tiling 3².4.3.4, in both “overlap” and “gap” regions, with small orthorhombic distortions imposed as rational approximants of the two perpendicular lattices. The three-dimensional structure is a periodic, rotating stack of gap and overlap regions, with a ten-fold rotation symmetry.

Acknowledgements

The authors acknowledge the financial support of the French Ministère délégué à la Recherche (Action Concertée Incitative 2000), through the ACI Biofrustration. We are indebted to Y. Bouligand for providing the impulse for this work, enlightening discussions, helpful suggestions, and for figures 1 and 5.