Nature of driving force for protein folding: A result from analyzing the statistical potential

In a statistical approach to protein structure analysis, Miyazawa and Jernigan derived a 20 X 20 matrix of inter-residue contact energies between different types of amino acids. Using the method of eigenvalue decomposition, we find that the Miyazawa-Jernigan matrix can be accurately reconstructed from its first two principal component vectors as M-ij = C-0 + C-1(q(i)) + q(i)) + C(2)q(i)q(i), 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.