O. Aichholzer, D. Bremner, E. Demaine, D. Meijer, V. Sacristán, and
M. Soss
It is widely accepted that (1) the natural or folded state of proteins is a
global energy minimum, and (2) in most cases proteins fold to a unique state
determined by their amino acid sequence. The H-P (hydrophobic-hydrophilic)
model is a simple combinatorial model designed to answer qualitative
questions about the protein folding process. In this paper we consider a
problem suggested by Brian Hayes in 1998: what proteins in the
two-dimensional H-P model have unique optimal (minimum energy)
foldings? In particular, we prove that there are closed chains of monomers
(amino acids) with this property for all (even) lengths; and that there are
open monomer chains with this property for all lengths divisible by four.