  We show that the hydrophobicity of sequences is the leading term in
Miyazawa-Jernigan interactions. Being the source of additive (solvation) terms
in pair-contact interactions, they were used to reduce the energy parameters
while resulting in a clear vector manipulation of energy. The reduced
(additive) potential performs considerably successful in predicting the
statistical properties of arbitrary structures. The evaluated designabilities
of the structures by both models are highly correlated. Suggesting
geometrically non-degenerate vectors (structures) as protein-like structures,
the additive model is a powerful tool for protein design. Moreover, a crossing
point in the log-linear diagram of designability-ranking shows that about 1/e
of the structures have designabilities above the average, independent on the
used model.
