Nature, 406 287-290 (2000)
Optimal shapes of compact strings
Amos Maritan, Cristian Micheletti, Antonio Trovato & Jayanth
R. Banavar
Link to online article.
ABSTRACT
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
problemÐthat 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.