Optimal geometrical arrangements, such as the stacking of atoms, are of
relevance in diverse disciplines(1-5). A classic problem is the
determination of the optimal arrangement of spheres in three dimensions
in order to achieve the highest packing fraction; only recently has it
been proved(1,2) that the answer for infinite systems is a
face-centred-cubic lattice. This simply stated problem has had a
profound impact in many areas(3-5), ranging from the crystallization and
melting of atomic systems, to optimal packing of objects and the
sub-division of space. Here we study an analogous problem-that of
determining the optimal shapes of closely packed compact strings. This
problem is a mathematical idealization of situations commonly
encountered in biology, chemistry and physics, involving the optimal
structure of folded polymeric chains. We rnd that, in cases where
boundary effects(6) are not dominant, helices with a particular
pitch-radius ratio are selected. Interestingly, the same geometry is
observed in helices in naturally occurring proteins.
