The transverse structure of collagen
Résumé
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 ?3 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 3^{2}.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.
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