  We investigate the extent to which the commonly used standard pairwise
contact potential can be used to identify the native fold of a protein. Ideally
one would hope that a universal energy function exists, for which the native
folds of all proteins are the respective ground states. Here we pose a much
more restricted question: is it possible to find a set of contact parameters
for which the energy of the native contact map of a single protein (crambin) is
lower than that of all possible physically realizable decoy maps. We seek such
a set of parameters by perceptron learning, a procedure which is guaranteed to
find such a set if it exists. We found that it is extremely hard (and most
probably, impossible) to fine tune contact parameters that will assign all
alternative conformations higher energy than that of the native map. This
finding clearly indicates that it is impossible to derive a general pairwise
contact potential that can be used to fold any given protein. Inclusion of
additional energy terms, such as hydrophobic (solvation), hydrogen bond or
multi-body interactions may help to attain foldability within specific
structural families.
