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 $20\times 20$ 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 $M_{\mathrm{ij}}{=C}_0{+C}_1\left(q_i{+q}_j\right){+C}_2{q}_i{q}_j$, 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.