  In a statistical approach to protein structure analysis, Miyazawa and
Jernigan (MJ) derived a $20\times 20$ matrix of inter-residue contact energies
between different types of amino acids. Using the method of eigenvalue
decomposition, we find that the MJ matrix can be accurately reconstructed from
its first two principal component vectors as $M_{ij}=C_0+C_1(q_i+q_j)+C_2 q_i
q_j$, with constant $C$'s, and 20 $q$ values associated with the 20 amino
acids. This regularity is due to hydrophobic interactions and a force of
demixing, the latter obeying Hildebrand's solubility theory of simple liquids.
