Conservation of statistical results under the reduction of pair-contact interactions to solvation interactions

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 nondegenerate vectors (structures) as proteinlike 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.