Boerdijk-Coxeter helix and biological helices as quasicrystals

Helices and dense packing of spherical objects are two closely related prob lems. The Boerdijk-Coxeter helix (B-C), a linear stacking of regular tetrah edra, is a very efficient solution to some close-packing problems, includin g protein folding. The structure of biological helices (alpha -helix, colla gen) is determined chiefly by steric repulsion. Thus, maximum density leads directly to structures related to the B-C helix. We show that the B-C heli x is a quasicrystalline structure with 1+root3 edges per turn, which can be disclinated and inflated. The collagen molecule consists of three intertwi ned helicoidal chains on the fibres of an inflated Hopf fibration. The cent ral core is a B-C helical packing of the hydrogen atoms side-groups of the amino acid Gly. (C) 2000 Elsevier Science B.V. All rights reserved.