Elusive Unfoldability: Learning a Contact Potential to Fold Crambin

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.