Changing a few contacts in a contact map corresponds to a large scale move
in confrontation space; hence, one gains a lot by using the contact map rep
resentation for protein folding. We developed an efficient search procedure
in the space of physical contact maps, which could identify the native fol
d as of the lowest free energy, provided on had a free energy function whos
e ground state is the native map. We prove rigorously that the widely used
pairwise contact approximation to the free energy cannot stabilize even a s
ingle protein's native map. Testing the native map against a set of decoys
obtained by gapless threading, one may be misled to the opposite conclusion
. [S0031-9007(98)08231-3].