Protein folding and inverse protein folding problems are examined for
the extremely simplified model of short self-avoiding square lattice w
alks involving only two or three residue types. Simple interresidue co
ntact free energy functions are given and are used to determine which
sequences fold uniquely to which conformations. Contrary to general th
eories of protein folding, this model system shows little correlation
between free energy and conformational distance from the native, nor i
s there any marked energy gap between the native and the best non-nati
ve structures. Furthermore, even the given free energy function someti
mes fails to identify which sequences fold to a particular target stru
cture. If current ideas about protein folding and structure/sequence c
ompatibility fail in this model system, it is unclear why they should
be valid for real proteins.