Nature, 406 287-290 (2000)

Optimal shapes of compact strings

Amos Maritan, Cristian Micheletti, Antonio Trovato & Jayanth R. Banavar

Link to online article.
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 crystalliza- tion 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 idealiza- tion of situations commonly encountered in biology, chemistry and physics, involving the optimal structure of folded polymeric chains. We find 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.