Ordering in dense fiber bundles, the phyllotactic solution and its application to collagen fibrils

The shape of the cross section of a dense fiber bundle is related to the symmetry of its molecular packing. However, this statement might be belied by type I collagen fibrils which have a rounded section of high symmetry while structural studies suggest that their molecules are assembled with a long range lateral order of lower symmetry. We examine how phyllotaxis, which is a non conventional crystallographic solution to packing efficiency in situations of high radial symmetry, can establish a link between those two apparently conflicting points. The lateral order imposed by the algorithm of phyllotaxis, which implies an enlargement of the notion of long range lateral order beyond that used for classical crystals, provides a basis for a new analysis of the experimental data.