To calculate the tertiary structure of a protein from its amino acid s
equence, the thermodynamic approach requires a potential function of s
equence and conformation that has its global minimum at the native con
formation for many different proteins. Here we study the behavior of s
uch functions for the simplest model system that still has some of the
features of the protein folding problem, namely two-dimensional squar
e lattice chain configurations involving two residue types. First we s
how that even the given contact potential, which by definition is used
to identify the folding sequences and their unique native conformatio
ns, cannot always correctly select which sequences will fold to a give
n structure. Second, we demonstrate that the given contact potential i
s not always able to favor the native alignment of a native sequence o
n its own native conformation over other gapped alignments of differen
t folding sequences onto that same conformation. Because of these shor
tcomings, even in this simple model system in which all conformations
and all native sequences are known and determined directly by the give
n potential, we must reexamine our expectations for empirical potentia
ls used for inverse folding and gapped alignment on more realistic rep
resentations of proteins. (C) 1996 Wiley-Liss, Inc.