Topology in Molecular Biology

148 N. Rivier and J.-F. Sadoc

Fig. 8.1.Structure of collagen at various scales. (a) Single chainGly−X−Yform-

ing a left-handed helix, with a curved axis.Dotsindicate the positions of successive

amino acids. Their side groups are pointing outwards; every third one is a glycine

(gly) located in the concave side of the axis. (b) A collagen molecule is a right-handed

triple helix of three intertwined polypeptide chains, each one being left-handed as in

(a). The core of the triple helix consists of the side groups of the glycines, a tightly

packed helix of H atoms. (c) A simpler representation of the right-handed triple

helix, represented more simply. Its width is 1 nm, its length 300 nm. (d) The colla-

gen molecule is often represented by an arrow of length 300 nm. (e) The molecules are

stacked on top of each other, with a gap of 35 nm, and regularly spaced on a lattice

(transverse scale dilated relative to longitudinal scale). The longitudinal coordinates

of moleculesuandu′are the same. One distinguishes gap and overlap levels,gand

o, respectively, so that to each five molecules inocorrespond only four ing(the ex-

tremities of the molecule lie at gap–overlap interfaces). There is a regular stagger of

molecules by a lengthD=g+o=67nm.(f) A crude representation of the lattice as

a cylinder (by identifyinguandu′). This is only schematic as the collagen fibril is a

lattice, showing the 67-nm stagger, but with a unit cell that accommodates gap and

overlap levels. Notice the right-handed chirality of theGlycore (see also Fig. 8.2 and

Fig. 8.4b) and of the triple-helix collagen molecule, opposite to the left-handed chi-

rality of the single collagen chain (polyproline II: PPII; see also Fig. 8.3). In Fig. 8.6

of [4], the PPII helix is wrongly drawn as right handed. We regret this oversight:

The figure, obtained from some public domain file, was added at the proof stage

The essential physical and geometrical features to be included in the struc-
ture of the collagen fibril are:
(a) Close packing of amino acids in a bundle of periodic, polypeptide chains
(b) Flexibility of the fibril, compatible with close packing